Variable Lebesgue Spaces and Hyperbolic Systems

種類:

電子ブック

責任表示:

by David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov

出版情報:

Basel : Springer Basel : Imprint: Birkhäuser, 2014

著者名:

Cruz-Uribe, David

Fiorenza, Alberto

Ruzhansky, Michael

Wirth, Jens

Tikhonov, Sergey

SpringerLink (Online service)

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シリーズ名:

Advanced Courses in Mathematics - CRM Barcelona ; 27

ISBN:

9783034808408 [3034808402]    

注記:

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 mor

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