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

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.

References in corpus (3)

• Harmonic Analysis Operators Associated with Multidimensional Bessel Operators
• Multivariate Spectral Multipliers
• Linear dimension-free estimates for the Hermite-Riesz transforms

Cited by in corpus (5)

• Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions
• Riesz Transforms and Spectral Multipliers of the Hodge-Laguerre Operator
• On derivatives, Riesz transforms and Sobolev spaces for Fourier-Bessel expansions
• Bellman Functions and Dimension Free $L^p$estimates for the Riesz Transforms in Bessel settings
• Joint spectral multipliers for mixed systems of operators