Sundaram Thangavelu, Yuan Xu
Abstract
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Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The $L^p$ boundedness of these operators is established in certain cases.
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Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The $L^p$ boundedness of these operators is established in certain cases.
Key concepts: Riesz transform, Riesz potential, Riesz representation theorem, Mathematics, M. Riesz extension theorem, Pure mathematics, Invariant (physics), Reflection (computer programming)