On Necessary And Sufficient Conditions For L P Estimates Of Riesz Transforms Associated To Elliptic Operators On Mathbb R N And Related Estimates

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On Necessary And Sufficient Conditions For L P Estimates Of Riesz Transforms Associated To Elliptic Operators On Mathbb R N And Related Estimates

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Author : Pascal Auscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

On Necessary And Sufficient Conditions For L P Estimates Of Riesz Transforms Associated To Elliptic Operators On Mathbb R N And Related Estimates written by Pascal Auscher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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 $(2,\infty)$.

History Of Banach Spaces And Linear Operators

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Author : Albrecht Pietsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31

History Of Banach Spaces And Linear Operators written by Albrecht Pietsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.

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.

The Analysis Of Linear Partial Differential Operators Iii

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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-15

The Analysis Of Linear Partial Differential Operators Iii written by Lars Hörmander and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-15 with Mathematics categories.

From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987. "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987.

Theory Of Besov Spaces

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Author : Yoshihiro Sawano
language : en
Publisher: Springer
Release Date : 2018-11-04

Theory Of Besov Spaces written by Yoshihiro Sawano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-04 with Mathematics categories.

This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

Harmonic Analysis On The Heisenberg Group

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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-24

Harmonic Analysis On The Heisenberg Group written by Sundaram Thangavelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-24 with Mathematics categories.

This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and, hence gives the greatest opportunity for generalizing the remarkable results of Euclidian harmonic analysis.

Sobolev Spaces

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Author : Vladimir Maz'ya
language : en
Publisher: Springer
Release Date : 2014-10-05

Sobolev Spaces written by Vladimir Maz'ya and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-05 with Mathematics categories.

The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q

Introduction To Operator Space Theory

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Author : Gilles Pisier
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-25

Introduction To Operator Space Theory written by Gilles Pisier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-25 with Mathematics categories.

The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C*-algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of 'length' of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer.

Riesz Transform Estimates In The Absence Of A Preservation Condition And Applications To The Dirichlet Laplacian

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Author : Joshua Grahame Peate
language : en
Publisher:
Release Date : 2015

Riesz Transform Estimates In The Absence Of A Preservation Condition And Applications To The Dirichlet Laplacian written by Joshua Grahame Peate and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Dirichlet forms categories.

Lp Estimates For Operators Associated To Oscillating Plane Curves

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Author : James Robert Wright
language : en
Publisher:
Release Date : 1990

Lp Estimates For Operators Associated To Oscillating Plane Curves written by James Robert Wright and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

A Priori Lp Estimates For The Solution Of The Navier Equations Of Elasticity Given The Forces On The Boundary

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Author : Angel Gutierrez
language : en
Publisher:
Release Date : 1979

A Priori Lp Estimates For The Solution Of The Navier Equations Of Elasticity Given The Forces On The Boundary written by Angel Gutierrez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.