Riesz transform and Riesz potentials for Dunkl transform

By S. Thangavelu, Yuan Xu. 2004

127 citations recorded by the source corpus.

Analogues of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weight functions that are invariant under a reflection group. The Lp boundedness of these operators is established in certain cases.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/35dadc25c3e9da6eadabe85d939a84873bf66bf8

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In Applied Mathematics

1. S. Tikhonov
2. Feng Dai
3. V. Ivanov
4. Heping Wang
5. Dmitry V. Gorbachev

Citations in the corpus

• Positive $$L^p$$Lp-Bounded Dunkl-Type Generalized Translation Operator and Its Applications (2017, methodology): “For 0 < α < 2λk + 2, the weighted Riesz potential I αf , is defined on S(Rd) (see [49]) by I αf(x) = (d α k ) −1 ∫”
• A transference theorem for the Dunkl transform and its applications (2010, background): “In fact, even the L boundedness of τy is not established in general (see [20, 19]).”