Calderón-Zygmund operators related to Jacobi expansions

Details Calderón-Zygmund operators related to Jacobi expansions Calderón-Zygmund operators related to Jacobi expansions

2010-11-16

arxiv.org/abs/1011.3615v1

Mathematics

Classical Analysis and ODEs

27 pages

Scientific paper

We study several fundamental operators in harmonic analysis related to Jacobi expansions, including Riesz transforms, imaginary powers of the Jacobi operator, the Jacobi-Poisson semigroup maximal operator and Littlewood-Paley-Stein square functions. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory. Our proofs rely on an explicit formula for the Jacobi-Poisson kernel, which we derive from a product formula for Jacobi polynomials.

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