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Calderón-Zygmund operators related to Jacobi expansions

Adam Nowak ; Peter Sjögren (Institutionen för matematiska vetenskaper)
Journal of Fourier Analysis and Applications (1069-5869). Vol. 18 (2012), 4, p. 717-749.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Jacobi polynomial, Jacobi expansion, Jacobi operator, Jacobi-Poisson semigroup, Riesz transform, Imaginary power, Maximal operator, Square function, Calderon-Zygmund operator



Denna post skapades 2010-12-03. Senast ändrad 2014-09-29.
CPL Pubid: 130013

 

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Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

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Matematik

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