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Abstract
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An explicit Bellman function is used to prove a bilinear embedding
theorem for operators associated with general multidimensional
orthogonal expansions on product spaces. This is then applied to obtain
boundedness,
, of appropriate
vectorial Riesz transforms, in particular in the case of Jacobi polynomials. Our estimates
for the
norms of these Riesz transforms are both dimension-free and linear in
. The
approach we present allows us to avoid the use of both differential forms and general
spectral multipliers.
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Keywords
Riesz transform, Bellman function, orthogonal expansion
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Mathematical Subject Classification 2010
Primary: 42C10, 42A50, 33C50
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Milestones
Received: 23 January 2017
Revised: 31 July 2017
Accepted: 23 September 2017
Published: 22 November 2017
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