The Hardy Inequality

Author : Karl-Goswin Grosse-Erdmann
Publisher : Springer Science & Business Media
Page : 132 pages
File Size : 49,7 Mb
Release : 1998-01-19
Category : Mathematics
ISBN : 3540639020

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.

Author : Michael Ruzhansky,Durvudkhan Suragan
Publisher : Springer
Page : 579 pages
File Size : 41,7 Mb
Release : 2019-07-02
Category : Mathematics
ISBN : 9783030028954

Get Book

Hardy Inequalities on Homogeneous Groups by Michael Ruzhansky,Durvudkhan Suragan Pdf

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Author : Alois Kufner,Lech Maligranda,Lars-Erik Persson
Publisher : Unknown
Page : 161 pages
File Size : 48,8 Mb
Release : 2007
Category : Electronic
ISBN : 8086843157

Get Book

The Hardy Inequality by Alois Kufner,Lech Maligranda,Lars-Erik Persson Pdf

Author : Alexander A. Balinsky,W. Desmond Evans,Roger T. Lewis
Publisher : Springer
Page : 263 pages
File Size : 41,5 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9783319228709

Get Book

The Analysis and Geometry of Hardy's Inequality by Alexander A. Balinsky,W. Desmond Evans,Roger T. Lewis Pdf

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.

Author : G. H. Hardy,J. E. Littlewood,George Pólya
Publisher : Cambridge University Press
Page : 344 pages
File Size : 46,6 Mb
Release : 1952
Category : Mathematics
ISBN : 0521358809

Get Book

Inequalities by G. H. Hardy,J. E. Littlewood,George Pólya Pdf

This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

Author : Dierk Schleicher,Malte Lackmann
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 45,7 Mb
Release : 2011-05-19
Category : Mathematics
ISBN : 9783642195334

Get Book

An Invitation to Mathematics by Dierk Schleicher,Malte Lackmann Pdf

This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization. Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.

Author : B. Opic,A. Kufner
Publisher : Unknown
Page : 351 pages
File Size : 55,6 Mb
Release : 1990-01-01
Category : Electronic
ISBN : 060803598X

Get Book

Hardy-Type Inequalities by B. Opic,A. Kufner Pdf

Author : Alois Kufner,Lars Erik Persson
Publisher : World Scientific
Page : 380 pages
File Size : 41,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9812381953

Get Book

Weighted Inequalities of Hardy Type by Alois Kufner,Lars Erik Persson Pdf

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.

Author : Alois Kufner,Lars-Erik Persson
Publisher : Unknown
Page : 16 pages
File Size : 45,5 Mb
Release : 2002
Category : Electronic
ISBN : OCLC:51710542

Get Book

The Hardy Inequality by Alois Kufner,Lars-Erik Persson Pdf

Author : Nassif Ghoussoub,Amir Moradifam
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 42,7 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 : Elijah Liflyand
Publisher : Springer Nature
Page : 199 pages
File Size : 50,6 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030818920

Get Book

Harmonic Analysis on the Real Line by Elijah Liflyand Pdf

This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.

Author : Alois Kufner,Lars-Erik Persson,Natasha Samko
Publisher : World Scientific Publishing Company
Page : 480 pages
File Size : 50,7 Mb
Release : 2017-06-16
Category : Electronic
ISBN : 9789813140660

Get Book

Weighted Inequalities of Hardy Type by Alois Kufner,Lars-Erik Persson,Natasha Samko Pdf

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy–Steklov operators, and some basic results about Hardy-type inequalities and their limit (Carleman–Knopp type) inequalities. It also describes some rather new areas such as higher order and fractional order Hardy-type inequalities and integral inequalities on the cone of monotone functions, together with some applications and open problems. In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions. Request Inspection Copy

Author : D. J. H. Garling
Publisher : Cambridge University Press
Page : 347 pages
File Size : 53,7 Mb
Release : 2007-07-05
Category : Mathematics
ISBN : 9781139465144

Get Book

Inequalities: A Journey into Linear Analysis by D. J. H. Garling Pdf

This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.

Author : Nikolai Kutev,Tsviatko Rangelov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 103 pages
File Size : 53,8 Mb
Release : 2022-10-24
Category : Mathematics
ISBN : 9783110980493

Get Book

Hardy Inequalities and Applications by Nikolai Kutev,Tsviatko Rangelov Pdf

This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.

Author : Everitt
Publisher : CRC Press
Page : 306 pages
File Size : 47,8 Mb
Release : 1990-11-30
Category : Mathematics
ISBN : 082478488X

Get Book

Inequalities by Everitt Pdf

Proceedings of an international conference organized by the London Mathematical Society, held July 1987 at the U. of Birmingham, and dominated by the ghosts of Hardy, Littlewood and Polya, whose Inequalities (still the primary reference in the field) appeared in 1934. Thirteen essays summarize subse