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Titlebook: Variable Lebesgue Spaces and Hyperbolic Systems; David Cruz-Uribe,Alberto Fiorenza,Jens Wirth,Serge Textbook 2014 Springer Basel 2014 Rubi

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书目名称Variable Lebesgue Spaces and Hyperbolic Systems
编辑David Cruz-Uribe,Alberto Fiorenza,Jens Wirth,Serge
视频video
概述Features a concise introduction to variable Lebesgue spaces requiring only basic knowledge of analysis.Includes an easy-to-read introduction to the classical problems as well as to recent developments
丛书名称Advanced Courses in Mathematics - CRM Barcelona
图书封面Titlebook: Variable Lebesgue Spaces and Hyperbolic Systems;  David Cruz-Uribe,Alberto Fiorenza,Jens Wirth,Serge Textbook 2014 Springer Basel 2014 Rubi
描述.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 more technical proofs and background material omitted. .Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent
出版日期Textbook 2014
关键词Rubio de Francia extrapolation; hyperbolic Cauchy problems; maximal operators; oscillating time-depende
版次1
doihttps://doi.org/10.1007/978-3-0348-0840-8
isbn_softcover978-3-0348-0839-2
isbn_ebook978-3-0348-0840-8Series ISSN 2297-0304 Series E-ISSN 2297-0312
issn_series 2297-0304
copyrightSpringer Basel 2014
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Properties of Variable Lebesgue Spacesctions. We then define the modular and the norm, and prove that .. is a Banach space. We prove a version of Hölder’s inequality, define the associate norm, and then characterize the dual space when .... We conclude with a version of the Lebesgue differentiation theorem.
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The Hardy–Littlewood Maximal Operatory–Littlewood maximal operator to be bounded on ..; in the next chapter we will show how this can be used to prove norm inequalities on .. for the other classical operators of harmonic analysis. We begin with a brief review of the maximal operator on the classical Lebesgue spaces and introduce our pr
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Extrapolation in Variable Lebesgue Spaces powerful generalization of the Rubio de Francia extrapolation theorem. This approach, first developed in [22] and then treated as part of a more general framework in [27], lets us use the theory of weighted norm inequalities to prove the corresponding estimates in variable Lebesgue spaces. This gre
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Equations with constant coefficientsquations with constant coefficients. One of the very helpful observations available in this case is that after a Fourier transform in the spatial variable . we obtain an ordinary differential equation with constant coefficients which can be solved almost explicitly once we know its characteristics.
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Extrapolation in Variable Lebesgue Spacesral framework in [27], lets us use the theory of weighted norm inequalities to prove the corresponding estimates in variable Lebesgue spaces. This greatly reduces the work required, since it lets us use the well-developed theory of weights.
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