Weighted Solyanik Estimates for the Hardy–Littlewood Maximal Operator and Embedding of A into Ap

Paul Hagelstein*, Ioannis Parissis

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

Let w denote a weight in ℝn which belongs to the Muckenhoupt class A and let Mw denote the uncentered Hardy–Littlewood maximal operator defined with respect to the measure w(x)dx. The sharp Tauberian constant of Mw with respect to α, denoted by Cw(α), is defined by (Formula presented.). In this paper, we show that the Solyanik estimate (Formula presented.) holds. Following the classical theme of weighted norm inequalities we also consider the sharp Tauberian constants defined with respect to the usual uncentered Hardy–Littlewood maximal operator M and a weight w: (Formula presented.). We show that we have (Formula presented.) if and only if w ∈ A. As a corollary of our methods we obtain a quantitative embedding of A into Ap.

Original languageEnglish
Pages (from-to)924-946
Number of pages23
JournalJOURNAL OF GEOMETRIC ANALYSIS
Volume26
Issue number2
DOIs
Publication statusPublished - 1 Apr 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Doubling measure
  • Halo function
  • Maximal function
  • Muckenhoupt weights
  • Tauberian conditions

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