Dimension free Lp estimates for single Riesz transforms via an H∞ joint functional calculus

By using an H-infinity 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. (C) 2014 Elsevier Inc. All rights reserved.