Calderón-Zygmund operators related to Jacobi expansions
Artikel i vetenskaplig tidskrift, 2012

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) Calderón-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.

Maximal operator

Calderon-Zygmund operator

Square function

Jacobi operator

Riesz transform

Jacobi expansion

Jacobi-Poisson semigroup

Imaginary power

Jacobi polynomial


Adam Nowak

Wrocław University of Science and Technology

Institute of Mathematics of the Polish Academy of Sciences

Peter Sjögren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Fourier Analysis and Applications

1069-5869 (ISSN)

Vol. 18 717-749