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Function Spaces and Partial Differential EquationsVolume 2: Contemporary Analysis$
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Ali Taheri

Print publication date: 2015

Print ISBN-13: 9780198733157

Published to Oxford Scholarship Online: September 2015

DOI: 10.1093/acprof:oso/9780198733157.001.0001

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Maximal Function; Bounding Averages and Pointwise Convergence

Maximal Function; Bounding Averages and Pointwise Convergence

Chapter:
(p.501) 13 Maximal Function; Bounding Averages and Pointwise Convergence
Source:
Function Spaces and Partial Differential Equations
Author(s):

Ali Taheri

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198733157.003.0013

This chapter introduces the Hardy-Littlewood maximal functions and establishes its bounded properties in various Lebesgue and Marcinkiewicz type spaces. The chapter also presents many applications to differentiability and a.e. convergence.

Keywords:   Vitali covering lemma, Hardy-Littlewood maximal function, Lebesgue spaces, Riesz potentials, Young’s convolution inequality, Stein’s theorem, Fourier restriction theorems, vector-valued inequalities

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