Weak type (1, 1) inequalities for discrete rough maximal functions

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Abstract

The aim of this paper is to show that the discrete maximal function (Formula Presented.), where Nh = {n ∈ ℕ: there exists m ∈ ℕ such that n = ⌊h(m)⌋} for an appropriate function h, is of weak type (1, 1). As a consequence, we also obtain a pointwise ergodic theorem along the set Nh.

Original languageEnglish (US)
Pages (from-to)247-281
Number of pages35
JournalJournal d'Analyse Mathematique
Volume127
Issue number1
DOIs
StatePublished - Sep 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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