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Juha Kinnunen, Juha Lehrback, "Maximal Function Methods for Sobolev Spaces"
English | ISBN: 1470465752 | 2021 | 354 pages | PDF | 2 MB
There are many good texts on using maximal functions in harmonic analysis, but Kinnunen, Lehrbäck, and Vähäkangas felt that there was room for a source book gathering developments in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximations for Sobolev functions, Hardy's inequalities, and partial differential equations. A recurring theme throughout the book is self-improvement of uniform quantitative conditions, they say, and they restrict their attention to prototypes in Euclidean spaces to avoid extra complication.

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