Discrete harmonic analysis associated with ultraspherical expansions
Classical Analysis and ODEs
2023-10-26 v1 Functional Analysis
Abstract
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 certain difference operator. We also prove weighted l^p-boundedness properties of transplantation operators associated to the system of ultraspherical functions. In order to show our results we previously establish a vector-valued local Calder\'on-Zygmund theorem in our discrete setting.
Cite
@article{arxiv.1512.01379,
title = {Discrete harmonic analysis associated with ultraspherical expansions},
author = {Jorge J. Betancor and Alejandro J. Castro and Juan C. Fariña and Lourdes Rodríguez-Mesa},
journal= {arXiv preprint arXiv:1512.01379},
year = {2023}
}