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...

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Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2009
Автори: Ben Salem, Nejib, Samaali, Taha
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2009
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
id nasplib_isofts_kiev_ua-123456789-149169
record_format dspace
spelling Ben Salem, Nejib
Samaali, Taha
2019-02-19T17:59:50Z
2019-02-19T17:59:50Z
2009
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.
1815-0659
2000 Mathematics Subject Classification: 42A50; 42C10
https://nasplib.isofts.kiev.ua/handle/123456789/149169
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.
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.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Hilbert Transforms Associated with Dunkl-Hermite Polynomials
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Hilbert Transforms Associated with Dunkl-Hermite Polynomials
spellingShingle Hilbert Transforms Associated with Dunkl-Hermite Polynomials
Ben Salem, Nejib
Samaali, Taha
title_short Hilbert Transforms Associated with Dunkl-Hermite Polynomials
title_full Hilbert Transforms Associated with Dunkl-Hermite Polynomials
title_fullStr Hilbert Transforms Associated with Dunkl-Hermite Polynomials
title_full_unstemmed Hilbert Transforms Associated with Dunkl-Hermite Polynomials
title_sort hilbert transforms associated with dunkl-hermite polynomials
author Ben Salem, Nejib
Samaali, Taha
author_facet Ben Salem, Nejib
Samaali, Taha
publishDate 2009
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description 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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149169
citation_txt 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.
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