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arXiv · 1404.6921

Dimension free $L^p$ estimates for Riesz transforms via an $H^{\infty}$ joint functional calculus

Błażej Wróbel
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Abstract

By using an $H^{\infty}$ joint functional calculus for strongly commuting operators, we derive a scheme to deduce the $L^p$ boundedness of certain $d$-dimensional Riesz transforms from the $L^p$ boundedness of appropriate one-dimensional Riesz transforms. Moreover, the $L^p$ bounds we obtain are independent of the dimension. The scheme is applied to Riesz transforms connected with orthogonal expansions and discrete Riesz transforms on products of groups with polynomial growth.

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BibTeXRIS

Błażej Wróbel. 2014-04-28. Dimension free $L^p$ estimates for Riesz transforms via an $H^{\infty}$ joint functional calculus. https://doi.org/10.1016/j.jfa.2014.07.005

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