Endpoint estimates for some maximal operators associated to the circular conical surface

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1 Citation (Scopus)

Abstract

For ψ ∈ C0 (Rd) and m > 0 we consider the maximal operator given byMm f (x, t) = under(sup, r > 0) | under(∫, Rd) f (x - y, t - | y |m) frac(1, rd) ψ (frac(y, r)) d y | . It is well known that Mm is a Lp-bounded operator for 1 < p ≤ ∞. Also A. Seeger and T. Tao proved that Mm is of weak-type L log log L if m ≠ 1. In this paper we consider the case m = 1 and prove M1 maps the standard Hardy space H1 to weak L1 if d ≥ 4.

Original languageEnglish
Pages (from-to)152-162
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume351
Issue number1
DOIs
Publication statusPublished - 2009 Mar 1
Externally publishedYes

Keywords

  • Maximal functions
  • Singular integrals

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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