Function Spaces And Inequalities

Author : Pankaj Jain,Hans-Jürgen Schmeisser
Publisher : Springer
Page : 335 pages
File Size : 48,5 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789811061196

Get Book

Function Spaces and Inequalities by Pankaj Jain,Hans-Jürgen Schmeisser Pdf

This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.

Author : B. Malcolm Brown,Jan Lang,Ian G. Wood
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 40,8 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 9783034802635

Get Book

Spectral Theory, Function Spaces and Inequalities by B. Malcolm Brown,Jan Lang,Ian G. Wood Pdf

This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

Author : David Eric Edmunds
Publisher : CRC Press
Page : 296 pages
File Size : 51,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0849309387

Get Book

Function Spaces and Applications by David Eric Edmunds Pdf

Developed from the proceedings an international conference held in 1997, Function Spaces and Applications presents the work of leading mathematicians in the vital and rapidly growing field of functional analysis.

Author : B. Malcolm Brown,Jan Lang,Ian G. Wood
Publisher : Birkhäuser
Page : 264 pages
File Size : 43,5 Mb
Release : 2011-11-09
Category : Mathematics
ISBN : 3034802641

Get Book

Spectral Theory, Function Spaces and Inequalities by B. Malcolm Brown,Jan Lang,Ian G. Wood Pdf

This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

Author : Ari Laptev
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 48,9 Mb
Release : 2009-12-02
Category : Mathematics
ISBN : 9781441913418

Get Book

Around the Research of Vladimir Maz'ya I by Ari Laptev Pdf

The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.

Author : Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík
Publisher : Walter de Gruyter
Page : 495 pages
File Size : 47,8 Mb
Release : 2012-12-19
Category : Mathematics
ISBN : 9783110250428

Get Book

Function Spaces, 1 by Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík Pdf

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 51,5 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

Get Book

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 : V. N. Faddeeva
Publisher : Unknown
Page : 210 pages
File Size : 49,8 Mb
Release : 1968
Category : Function spaces
ISBN : STANFORD:36105002015530

Get Book

Numerical Methods and Inequalities in Function Spaces by V. N. Faddeeva Pdf

Author : Ali Taheri
Publisher : OUP Oxford
Page : 500 pages
File Size : 49,9 Mb
Release : 2015-07-30
Category : Mathematics
ISBN : 9780191047824

Get Book

Function Spaces and Partial Differential Equations by Ali Taheri Pdf

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Author : D. E. Edmunds,W. D. Evans
Publisher : Cambridge University Press
Page : 170 pages
File Size : 47,5 Mb
Release : 2022-10-13
Category : Mathematics
ISBN : 9781009254649

Get Book

Fractional Sobolev Spaces and Inequalities by D. E. Edmunds,W. D. Evans Pdf

The fractional Sobolev spaces studied in the book were introduced in the 1950s by Aronszajn, Gagliardo and Slobodeckij in an attempt to fill the gaps between the classical Sobolev spaces. They provide a natural home for solutions of a vast, and rapidly growing, number of questions involving differential equations and non-local effects, ranging from financial modelling to ultra-relativistic quantum mechanics, emphasising the need to be familiar with their fundamental properties and associated techniques. Following an account of the most basic properties of the fractional spaces, two celebrated inequalities, those of Hardy and Rellich, are discussed, first in classical format (for which a survey of the very extensive known results is given), and then in fractional versions. This book will be an Ideal resource for researchers and graduate students working on differential operators and boundary value problems.

Author : David R. Adams,Lars I. Hedberg
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662032824

Get Book

Function Spaces and Potential Theory by David R. Adams,Lars I. Hedberg Pdf

"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

Author : Kehe Zhu
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 41,5 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821839652

Get Book

Operator Theory in Function Spaces by Kehe Zhu Pdf

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Author : Nassif Ghoussoub,Amir Moradifam
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 44,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780821891520

Get Book

Functional Inequalities: New Perspectives and New Applications by Nassif Ghoussoub,Amir Moradifam Pdf

"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.

Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 51,6 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9783764375829

Get Book

Theory of Function Spaces III by Hans Triebel Pdf

This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.

Author : Karl-Goswin Grosse-Erdmann
Publisher : Springer
Page : 122 pages
File Size : 41,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696643

Get Book

The Blocking Technique, Weighted Mean Operators and Hardy's Inequality by Karl-Goswin Grosse-Erdmann Pdf

This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.