On Necessary And Sufficient Conditions For Lp Estimates Of Riesz Transforms Associated To Elliptic Operators On Mathbb Rn And Related Estimates
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Author | : Pascal Auscher |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 102 |
Release | : 2014-09-11 |
Genre | : MATHEMATICS |
ISBN | : 9781470404758 |
This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2, \infty)$.
Author | : Pascal Auscher |
Publisher | : American Mathematical Soc. |
Total Pages | : 102 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821839411 |
This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.
Author | : Joshua Grahame Peate |
Publisher | : |
Total Pages | : 182 |
Release | : 2015 |
Genre | : Dirichlet forms |
ISBN | : |
Author | : Yuri A. Kordyukov |
Publisher | : |
Total Pages | : 15 |
Release | : 1995 |
Genre | : |
ISBN | : |
Author | : James Robert Wright |
Publisher | : |
Total Pages | : 216 |
Release | : 1990 |
Genre | : |
ISBN | : |
Author | : Lawrence Craig Evans |
Publisher | : CRC Press |
Total Pages | : 314 |
Release | : 2015-04-17 |
Genre | : Mathematics |
ISBN | : 1482242397 |
This book emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the p- theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.
Author | : Albrecht Pietsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 877 |
Release | : 2007-12-31 |
Genre | : Mathematics |
ISBN | : 0817645969 |
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Author | : Lars Diening |
Publisher | : Springer |
Total Pages | : 516 |
Release | : 2011-03-29 |
Genre | : Mathematics |
ISBN | : 3642183638 |
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 V. Cruz-Uribe |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2013-02-12 |
Genre | : Mathematics |
ISBN | : 3034805489 |
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 | : Haim Brezis |
Publisher | : Springer Science & Business Media |
Total Pages | : 600 |
Release | : 2010-11-02 |
Genre | : Mathematics |
ISBN | : 0387709142 |
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.