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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149169 |
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| 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149169 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1491692019-02-20T01:27:16Z Hilbert Transforms Associated with Dunkl-Hermite Polynomials Ben Salem, Nejib Samaali, Taha 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149169 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Ben Salem, Nejib Samaali, Taha |
| spellingShingle |
Ben Salem, Nejib Samaali, Taha Hilbert Transforms Associated with Dunkl-Hermite Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ben Salem, Nejib Samaali, Taha |
| author_sort |
Ben Salem, Nejib |
| title |
Hilbert Transforms Associated with Dunkl-Hermite Polynomials |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT bensalemnejib hilberttransformsassociatedwithdunklhermitepolynomials AT samaalitaha hilberttransformsassociatedwithdunklhermitepolynomials |
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2023-05-20T17:32:29Z |
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2023-05-20T17:32:29Z |
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1796153527403282432 |