Maximal functions and singular integrals associated to polynomial mappings of IRn

A Carbery, Fulvio Ricci, J Wright

Research output: Contribution to journalArticlepeer-review

Abstract

We consider convolution operators on R-n of the form

T(P)f(x) = integral(Rm) f(x - P(y))K(y)dy,

where P is a polynomial defined on R-m with values in R-n and K is a smooth Calderon-Zygmund kernel on R-m. A maximal operator M-P can be constructed in a similar fashion. We discuss weak-type 1-1 estimates for T-P and M-P and the uniformity of such estimates with respect to P. We also obtain L-p-estimates for "supermaximar' operators, defined by taking suprema over P ranging in certain classes of polynomials of bounded degree.

Original languageEnglish
Pages (from-to)122
Number of pages22
JournalRevista Matemática Iberoamericana
Volume19
Issue number1
Publication statusPublished - 2003

Keywords

  • maximal functions
  • singular integrals
  • weak-type estimates
  • HILBERT-TRANSFORMS
  • HARMONIC-ANALYSIS
  • NILPOTENT GROUPS
  • ROUGH OPERATORS
  • KERNELS
  • BOUNDS

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