Discrete harmonic analysis associated with ultraspherical expansions
arXiv:1512.01379 · doi:10.1007/s11118-019-09777-9
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 Calderón-Zygmund theorem in our discrete setting.