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 L2. Following them, we give easy to check suficient conditions for their boundedness on Lp, 1 < p < 1. We also discuss the symmetrized version of these transforms.
Lp boundedness of Riesz transforms for orthogonal polynomials in a general context
SASSO, EMANUELA;
2015-01-01
Abstract
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 L2. Following them, we give easy to check suficient conditions for their boundedness on Lp, 1 < p < 1. We also discuss the symmetrized version of these transforms.
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