There are many good texts on using maximal functions in harmonic analysis, but Kinnunen, Lehrb�ck, and V�h�kangas felt that there was room for a source book gathering developments in maximal function methods related to Poincar� 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. Annotation �2021 Ringgold, Inc., Portland, OR (protoview.com)

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