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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | 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 |
| Zitieren: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725370751483904 |
|---|---|
| author | Ben Salem, Nejib Samaali, Taha |
| author_facet | Ben Salem, Nejib Samaali, Taha |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T18:52:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149169 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:52:20Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Hilbert Transforms Associated with Dunkl-Hermite Polynomials Ben Salem, Nejib Samaali, Taha |
| title | 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_short | Hilbert Transforms Associated with Dunkl-Hermite Polynomials |
| title_sort | hilbert transforms associated with dunkl-hermite polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149169 |
| work_keys_str_mv | AT bensalemnejib hilberttransformsassociatedwithdunklhermitepolynomials AT samaalitaha hilberttransformsassociatedwithdunklhermitepolynomials |