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

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
JournalPotential Analysis
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Harmonic Analysis
Boundedness
Heat Semigroup
Transplantation
Orthogonal Functions
Maximal Operator
Difference Operator
G-function
Eigenfunctions
Siméon Denis Poisson
Operator
Theorem
Family

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Betancor, J. J., Castro Castilla, A. J., Fariña, J. C., & Rodríguez-Mesa, L. (2019). Discrete Harmonic Analysis Associated with Ultraspherical Expansions. Potential Analysis. https://doi.org/10.1007/s11118-019-09777-9

Discrete Harmonic Analysis Associated with Ultraspherical Expansions. / Betancor, Jorge J.; Castro Castilla, Alejandro J.; Fariña, Juan C.; Rodríguez-Mesa, L.

In: Potential Analysis, 01.01.2019.

Research output: Contribution to journalArticle

Betancor, Jorge J. ; Castro Castilla, Alejandro J. ; Fariña, Juan C. ; Rodríguez-Mesa, L. / Discrete Harmonic Analysis Associated with Ultraspherical Expansions. In: Potential Analysis. 2019.
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