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.
Jacobi operator
Riesz transform
Jacobi polynomial
Jacobi expansion
Square function
Calderon-Zygmund operator
Maximal operator
Imaginary power
Jacobi-Poisson semigroup
Författare
Adam Nowak
Polish Academy of Sciences
Politechnika Wrocławska
Peter Sjögren
Chalmers, Matematiska vetenskaper, Matematik
Göteborgs universitet
Journal of Fourier Analysis and Applications
1069-5869 (ISSN) 15315851 (eISSN)
Vol. 18 4 717-749Ämneskategorier
Matematik
DOI
10.1007/s00041-012-9217-6