Mixed-norm estimates for a class of nonisotropic directional maximal operators and Hilbert transforms

Richard Bez

Research output: Contribution to journalArticle

2 Citations (Scopus)
142 Downloads (Pure)

Abstract

For all d >= 2 and P epsilon (1, max(2, (d + 1)/2)], we prove sharp L-p to L-p(L-q) estimates (modulo an endpoint) for a directional maximal operator associated to curves generated by the dilation matrices exp((log t)P), where P has real entries and eigenvalues with positive real part. For the corresponding Hilbert transform we prove an analogous result for all d >= 2 and P epsilon (1, 2]. As corollaries, we prove L-p bounds for variable kernel singular integral operators and Nikodym-type maximal operators taking averages over certain families of curved sets in R-d. (C) 2008 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)3281-3302
Number of pages22
JournalJournal of Functional Analysis
Volume255
Issue number12
DOIs
Publication statusPublished - 15 Dec 2008

Keywords

  • Nonisotropic
  • Mixed-norm estimates
  • Hilbert transform
  • Maximal operator

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