An extrapolation theorem with applications to weighted estimates for singular integrals

Andrei K. Lerner, Sheldy Ombrosi

Research output: Contribution to journalArticlepeer-review

Abstract

We prove an extrapolation theorem saying that the weighted weak type (1, 1) inequality for A 1 weights implies the strong L p(w) bound in terms of the L p(w) operator norm of the maximal operator M. The weak Muckenhoupt-Wheeden conjecture along with this result allows us to conjecture that the following estimate holds for a Calderón-Zygmund operator T for any p>1: The latter conjecture would yield the sharp estimates for ||T||L p(w) in terms of the A q characteristic of w for any 1<q<p. In this paper we get a weaker inequality with the corresponding estimates for ||w||A q when 1<q<p.

Original languageEnglish
Pages (from-to)4475-4487
Number of pages13
JournalJournal of Functional Analysis
Volume262
Issue number10
DOIs
StatePublished - 15 May 2012

Keywords

  • Maximal functions
  • Singular integrals
  • Weighted inequalities

All Science Journal Classification (ASJC) codes

  • Analysis

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