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Hilbert Transforms Associated with Dunkl-Hermite Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Hilbert Transforms Associated with Dunkl-Hermite Polynomials
Інший ID:
2000 Mathematics Subject Classification: 42A50; 42C10
Посилання:
Hilbert Transforms Associated with Dunkl-Hermite Polynomials / N.B. Salem, T. Samaali // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 12 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The authors thank the anonymous referees for their careful reading of the manuscript and their valuable suggestions to improve the style of this paper.
Дата:
2009
Переглядів:
382
Завантажень:
231
Анотація:
We consider expansions of functions in Lp(R,|x|2kdx), 1 ≤ p < +∞ with respect to Dunkl-Hermite functions in the rank-one setting. We actually define the heat-diffusion and Poisson integrals in the one-dimensional Dunkl setting and study their properties. Next, we define and deal with Hilbert transforms and conjugate Poisson integrals in the same setting. The formers occur to be Calderón-Zygmund operators and hence their mapping properties follow from general results.
