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Mixed norm estimates for the Riesz transforms on $$\mathrm{SU}(2)$$. (English) Zbl 1344.42025
Authors’ abstract: In this paper we prove mixed norm estimates for Riesz transforms on the group $$\mathrm{SU}(2)$$. From these results vector valued inequalities for sequences of Riesz transforms associated to Jacobi differential operators of different types are deduced.
##### MSC:
 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 47G40 Potential operators 26A33 Fractional derivatives and integrals 43A90 Harmonic analysis and spherical functions 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35 Function spaces arising in harmonic analysis 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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