Some remarks on Lp-Lq estimates for some singular fractional integral operators

Research output: Contribution to journalArticle

Abstract

Let d ≥ 2 and let η : Rd - 1 → R be a smooth function which is supported in [- 1, 1]d - 1. Suppose μ is the measure on Rd given byμ (E) = under(∫, Rd - 1) χE (x, φ (x)) η (x) d x with φ (x) = ∑i = 1 d - 1 ± | xi |ai, 1 ≠ ai ∈ R. In this paper we study the Lp-Lq estimates for singular fractional integral operators given byA f (x) = under(∫, Rd) f (x - y) (underover(∏, i = 1, d - 1) | yi |γi - 1) d μ (y) with 0 < γi.

Original languageEnglish
Pages (from-to)407-417
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume332
Issue number1
DOIs
Publication statusPublished - 2007 Aug 1
Externally publishedYes

Keywords

  • Fractional integral operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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