Variable Lebesgue Spaces

Author : David V. Cruz-Uribe,Alberto Fiorenza
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 47,7 Mb
Release : 2013-02-12
Category : Mathematics
ISBN : 9783034805483

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Variable Lebesgue Spaces by David V. Cruz-Uribe,Alberto Fiorenza Pdf

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.​

Author : Springer
Publisher : Unknown
Page : 324 pages
File Size : 55,6 Mb
Release : 2013-02-12
Category : Electronic
ISBN : 3034805497

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Variable Lebesgue Spaces by Springer Pdf

Author : Lars Diening,Petteri Harjulehto,Peter Hästö,Michael Ruzicka
Publisher : Springer
Page : 509 pages
File Size : 55,7 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642183638

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Lebesgue and Sobolev Spaces with Variable Exponents by Lars Diening,Petteri Harjulehto,Peter Hästö,Michael Ruzicka Pdf

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Author : Rene Erlin Castillo,Humberto Rafeiro
Publisher : Springer
Page : 461 pages
File Size : 41,5 Mb
Release : 2016-06-23
Category : Mathematics
ISBN : 9783319300344

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An Introductory Course in Lebesgue Spaces by Rene Erlin Castillo,Humberto Rafeiro Pdf

This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.

Author : Lars Diening
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 44,8 Mb
Release : 2011-03-31
Category : Mathematics
ISBN : 9783642183621

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Lebesgue and Sobolev Spaces with Variable Exponents by Lars Diening Pdf

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Author : David Cruz-Uribe,Alberto Fiorenza,Michael Ruzhansky,Jens Wirth
Publisher : Springer
Page : 170 pages
File Size : 47,7 Mb
Release : 2014-07-22
Category : Mathematics
ISBN : 9783034808408

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Variable Lebesgue Spaces and Hyperbolic Systems by David Cruz-Uribe,Alberto Fiorenza,Michael Ruzhansky,Jens Wirth Pdf

This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.

Author : Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko
Publisher : Birkhäuser
Page : 567 pages
File Size : 53,9 Mb
Release : 2016-05-11
Category : Mathematics
ISBN : 9783319210155

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Integral Operators in Non-Standard Function Spaces by Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko Pdf

This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Author : Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim
Publisher : CRC Press
Page : 316 pages
File Size : 52,5 Mb
Release : 2020-09-16
Category : Mathematics
ISBN : 9781000064070

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Morrey Spaces by Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim Pdf

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Author : Matteo Pastorino
Publisher : John Wiley & Sons
Page : 367 pages
File Size : 42,8 Mb
Release : 2010-04-27
Category : Technology & Engineering
ISBN : 9780470602478

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Microwave Imaging by Matteo Pastorino Pdf

An introduction to the most relevant theoretical and algorithmic aspects of modern microwave imaging approaches Microwave imaging—a technique used in sensing a given scene by means of interrogating microwaves—has recently proven its usefulness in providing excellent diagnostic capabilities in several areas, including civil and industrial engineering, nondestructive testing and evaluation, geophysical prospecting, and biomedical engineering. Microwave Imaging offers comprehensive descriptions of the most important techniques so far proposed for short-range microwave imaging—including reconstruction procedures and imaging systems and apparatus—enabling the reader to use microwaves for diagnostic purposes in a wide range of applications. This hands-on resource features: A review of the electromagnetic inverse scattering problem formulation, written from an engineering perspective and with notations The most effective reconstruction techniques based on diffracted waves, including time- and frequency-domain methods, as well as deterministic and stochastic space-domain procedures Currently proposed imaging apparatus, aimed at fast and accurate measurements of the scattered field data Insight on near field probes, microwave axial tomographs, and microwave cameras and scanners A discussion of practical applications with detailed descriptions and discussions of several specific examples (e.g., materials evaluation, crack detection, inspection of civil and industrial structures, subsurface detection, and medical applications) A look at emerging techniques and future trends Microwave Imaging is a practical resource for engineers, scientists, researchers, and professors in the fields of civil and industrial engineering, nondestructive testing and evaluation, geophysical prospecting, and biomedical engineering.

Author : Petteri Harjulehto,Peter Hästö
Publisher : Springer
Page : 169 pages
File Size : 54,9 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9783030151003

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Orlicz Spaces and Generalized Orlicz Spaces by Petteri Harjulehto,Peter Hästö Pdf

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.

Author : Juha Heinonen
Publisher : Springer Science & Business Media
Page : 149 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301318

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Lectures on Analysis on Metric Spaces by Juha Heinonen Pdf

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.

Author : Giovanni Leoni
Publisher : American Mathematical Soc.
Page : 626 pages
File Size : 42,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847688

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A First Course in Sobolev Spaces by Giovanni Leoni Pdf

Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the book makes it suitable for advanced undergraduates or beginning graduate students. Moreover, the one-variable part of the book helps to develop a solid background that facilitates the reading and understanding of Sobolev functions of several variables. The second part of the book is more classical, although it also contains some recent results. Besides the standard results on Sobolev functions, this part of the book includes chapters on BV functions, symmetric rearrangement, and Besov spaces. The book contains over 200 exercises.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 41,6 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Author : Erhan Pişkin,Baver Okutmuştur
Publisher : Bentham Science Publishers
Page : 203 pages
File Size : 48,8 Mb
Release : 2021-11-10
Category : Mathematics
ISBN : 9781681089140

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An Introduction to Sobolev Spaces by Erhan Pişkin,Baver Okutmuştur Pdf

Sobolev spaces were firstly defined by the Russian mathematician, Sergei L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces have been studied by mathematicians until today. Functions that account for existence and uniqueness, asymptotic behavior, blow up, stability and instability of the solution of many differential equations that occur in applied and in engineering sciences are carried out with the help of Sobolev spaces and embedding theorems in these spaces. An Introduction to Sobolev Spaces provides a brief introduction to Sobolev spaces at a simple level with illustrated examples. Readers will learn about the properties of these types of vector spaces and gain an understanding of advanced differential calculus and partial difference equations that are related to this topic. The contents of the book are suitable for undergraduate and graduate students, mathematicians, and engineers who have an interest in getting a quick, but carefully presented, mathematically sound, basic knowledge about Sobolev Spaces.

Author : Nancy Kress
Publisher : Tor Books
Page : 368 pages
File Size : 52,8 Mb
Release : 2004-01-05
Category : Fiction
ISBN : 9781466825253

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Probability Space by Nancy Kress Pdf

Nancy Kress cemented her reputation in SF with the publication of her multiple-award–winning novella, "Beggars in Spain," which became the basis for her extremely successful Beggars Trilogy (comprising Beggars in Spain, Beggars and Choosers, and Beggars Ride). And now she brings us Probability Space, the conclusion of the trilogy that began with Probability Moon and then Probability Sun, which is centered on the same world as Kress's Nebula Award-winning novelette, "Flowers of Aulit Prison." The Probability Trilogy has already been widely recognized as the next great work by this important SF writer. In Probability Space, humanity's war with the alien Fallers continues, and it is a war we are losing. Our implacable foes ignore all attempts at communication, and they take no prisoners. Our only hope lies with an unlikely coalition: Major Lyle Kaufman, retired warrior; Marbet Grant, the Sensitive who's involved with Kaufman; Amanda, a very confused fourteen-year-old girl; and Magdalena, one of the biggest power brokers in all of human space. As the action moves from Earth to Mars to the farthest reaches of known space, with civil unrest back home and alien war in deep space, four humans--armed with little more than an unproven theory--try to enter the Fallers' home star system. It's a desperate gamble, and the fate of the entire universe may hang in the balance. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.