Hilbert Transforms Associated with Dunkl-Hermite Polynomials
We consider expansions of functions in L^p(R,|x|^{2k}dx), 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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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-03-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.037 |
| _version_ | 1818833814379560960 |
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| author | Néjib Ben Salem Taha Samaali |
| author_facet | Néjib Ben Salem Taha Samaali |
| author_sort | Néjib Ben Salem |
| collection | DOAJ |
| description | We consider expansions of functions in L^p(R,|x|^{2k}dx), 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. |
| first_indexed | 2024-12-19T02:24:54Z |
| format | Article |
| id | doaj.art-e832c3d72fba49a5960d8a0921e6cc26 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-19T02:24:54Z |
| publishDate | 2009-03-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-e832c3d72fba49a5960d8a0921e6cc262022-12-21T20:40:00ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-03-015037Hilbert Transforms Associated with Dunkl-Hermite PolynomialsNéjib Ben SalemTaha SamaaliWe consider expansions of functions in L^p(R,|x|^{2k}dx), 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.http://dx.doi.org/10.3842/SIGMA.2009.037Dunkl operatorDunkl-Hermite functionsHilbert transformsconjugate Poisson integralsCalderón-Zygmund operators |
| spellingShingle | Néjib Ben Salem Taha Samaali Hilbert Transforms Associated with Dunkl-Hermite Polynomials Symmetry, Integrability and Geometry: Methods and Applications Dunkl operator Dunkl-Hermite functions Hilbert transforms conjugate Poisson integrals Calderón-Zygmund operators |
| 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 |
| topic | Dunkl operator Dunkl-Hermite functions Hilbert transforms conjugate Poisson integrals Calderón-Zygmund operators |
| url | http://dx.doi.org/10.3842/SIGMA.2009.037 |
| work_keys_str_mv | AT nejibbensalem hilberttransformsassociatedwithdunklhermitepolynomials AT tahasamaali hilberttransformsassociatedwithdunklhermitepolynomials |