The Hilbert transform for Dunkl differential operators associated to the reflection group \(\mathbb{Z}_2\)

DOI10.1007/s10476-023-0189-3OpenAlexW4317811814MaRDI QIDQ2694896

P. I. A. López

Publication date: 4 April 2023

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10476-023-0189-3

zbMATH Keywords

Hilbert transformCauchy-Riemann equationstruncated Hilbert transformDunkl operatorDunkl transformconjugate funcion

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Cites Work

• Linear and bilinear multiplier operators for the Dunkl transform
• Riesz transform and Riesz potentials for Dunkl transform
• Hilbert transforms associated with Dunkl-Hermite polynomials
• Convolution operator and maximal function for the Dunkl transform
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
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