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Dimension-free $L^p$
estimates for vectors of Riesz transforms associated with
orthogonal expansions
Błażej Wróbel |
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Vol. 11 (2018), No. 3, 745–773
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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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Authors |
| Błażej Wróbel | |
| Mathematical Institute Universität Bonn Bonn Germany |
Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland |
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