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      Dimension-free \(L^p\) estimates for vectors of Riesz transforms associated with orthogonal expansions

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          Abstract

          An explicit Bellman function is used to prove a bilinear embedding theorem for operators associated with general multi-dimensional orthogonal expansions on product spaces. This is then applied to obtain \(L^p,\) \(1<p<\infty,\) boundedness of appropriate vectorial Riesz transforms, in particular in the case of Jacobi polynomials. Our estimates for the \(L^p\) norms of these Riesz transforms are both dimension-free and linear in \(\max(p,p/(p-1)).\) The approach we present allows us to avoid the use of both differential forms and general spectral multipliers.

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          Most cited references14

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          Explorations in martingale theory and its applications

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            L p ?dimension free boundedness for Riesz transforms associated to Hermite functions ?

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              Transformations de riesz pour les lois gaussiennes

              P Meyer (1984)
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                Author and article information

                Journal
                2017-01-07
                Article
                1701.01889
                a7a593a7-d200-4507-9230-f0d4294dfd08

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                42C10, 42A50, 33C50
                math.FA

                Functional analysis
                Functional analysis

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