$L^p $ boundedness of Riesz transforms for orthogonal polynomials in a general context
Tom 231 / 2015
Studia Mathematica 231 (2015), 45-71 MSC: 42C05, 42C15. DOI: 10.4064/sm8221-1-2016 Opublikowany online: 10 February 2016
Nowak and Stempak (2006) proposed a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal expansions, and proved their boundedness on $L^2$. Following them, we give easy to check sufficient conditions for their boundedness on $L^p$, $1 \lt p \lt \infty $. We also discuss the symmetrized version of these transforms.