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Author Kinnunen, Juha, author
Title Maximal function methods for Sobolev spaces / Juha Kinnunen, Juha Lehrback, Antti Vahakangas
Imprint Providence, Rhode Island : American Mathematical Society, [2021]
book jacket
 Mathematics Library  QA323 .K56 2021    AVAILABLE    30340200570798
Descript xii, 338 pages ; 26 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
Series Mathematical surveys and monographs, 0076-5376 ; volume 257
Mathematical surveys and monographs ; no. 257
Note "This book discusses advances in maximal function methods related to Poincare and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Holder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations"-- Provided by publisher
Includes bibliographical references (pages 317-333) and index
Maximal functions -- Lipschitz and Sobolev functions -- Sobolev and Poincare inequalities -- Pointwise inequalities for Sobolev functions -- Capacities and fine properties of Sobolev functions -- Hardy's inequalities -- Density conditions -- Muckenhoupt weights -- Weighted maximal and Poincareinequalities -- Distance weights and Hardy-Sobolev inequalities -- The p-Laplace equation -- Stability results for the p-Laplace equation
Subject Sobolev spaces
Maximal functions
Inequalities (Mathematics)
Espaces de Sobolev
Fonctions maximales
Inequalities (Mathematics)
Inequalities (Mathematics) fast (OCoLC)fst00972020
Maximal functions. fast (OCoLC)fst01012621
Sobolev spaces. fast (OCoLC)fst01122115
Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory. msc
Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems. msc
Real functions -- Inequalities -- Inequalities involving derivatives and differential and integral operators. msc
Measure and integration -- Classical measure theory -- Contents, measures, outer measures, capacities. msc
Potential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length and related notions in higher dimensions. msc
Partial differential equations -- General topics in partial differential equations -- Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals. msc
Partial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-Laplacian. msc
Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE. msc
Alt Author Lehrback, Juha (Juha Tapio), 1979- author
Vahakangas, Antti V., author
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