Hilbert Transforms Associated with Dunkl-Hermite Polynomials
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 tran...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149169 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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.
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| ISSN: | 1815-0659 |