Abstract
We define Riesz transforms and conjugate Poisson integrals associated with multi-dimensional Jacobi expansions. Under a slight restriction on the type parameters, we prove that these operators are bounded in L p, 1 < p < ∞, with constants independent of the dimension. Our tools are suitably defined g-functions and Littlewood-Paley-Stein theory, involving the Jacobi-Poisson semigroup and modifications of it.
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Research of both authors supported by the European Commission via the Research Training Network “Harmonic Analysis and Related Problems”, contract HPRN-CT-2001-00273-HARP.
The first-named author was also supported by MNiSW Grant N201 054 32/4285.
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Nowak, A., Sjögren, P. Riesz transforms for Jacobi expansions. J Anal Math 104, 341–369 (2008). https://doi.org/10.1007/s11854-008-0027-3
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DOI: https://doi.org/10.1007/s11854-008-0027-3