Discrete Harmonic Analysis Associated with Ultraspherical Expansions

Jorge J. Betancor, Alejandro J. Castro Castilla, Juan C. Fariña, L. Rodríguez-Mesa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l p -boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated by the difference operator ??f(n):=an?f(n+1)-2f(n)+an-1?f(n-1),n?N,?>0,where an?:={(2?+n)(n+1)/[(n+?)(n+1+?)]}1/2, n? N, and a-1?:=0. We also prove weighted l p -boundedness properties of transplantation operators associated with the system {fn?}n?N of ultraspherical functions, a family of eigenfunctions of ? ? . In order to show our results we previously establish a vector-valued local Calderón-Zygmund theorem in our discrete setting.

Original languageEnglish
Pages (from-to)523-563
JournalPotential Analysis
Volume53
Issue number2
DOIs
Publication statusPublished - Jan 1 2019

Keywords

  • Calderón-Zygmund
  • Littlewood-Paley functions
  • Maximal operators
  • Transplantation operators
  • Ultraspherical functions

ASJC Scopus subject areas

  • Analysis

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