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arXiv · 1512.01379

Discrete harmonic analysis associated with ultraspherical expansions

Jorge J. Betancor·Alejandro J. Castro·Juan C. Fariña·Lourdes Rodríguez-Mesa
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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.

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Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña, Lourdes Rodríguez-Mesa. 2015-12-04. Discrete harmonic analysis associated with ultraspherical expansions. https://doi.org/10.1007/s11118-019-09777-9

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