On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to Zd2. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, g-fu...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147861 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings / A. Nowak, K. Stempak, T.Z. Szarek // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 46 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718998015115264 |
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| author | Nowak, A. Stempak, K. Szarek, T.Z. |
| author_facet | Nowak, A. Stempak, K. Szarek, T.Z. |
| citation_txt | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings / A. Nowak, K. Stempak, T.Z. Szarek // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 46 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to Zd2. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, g-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes type. By means of the general Calderón-Zygmund theory we prove that these operators are bounded on weighted Lp spaces, 1 < p < ∞, and from weighted L1 to weighted weak L1. We also obtain similar results for analogous set of operators in the closely related multi-dimensional Laguerre-symmetrized framework. The latter emerges from a symmetrization procedure proposed recently by the first two authors. As a by-product of the main developments we get some new results in the multi-dimensional Laguerre function setting of convolution type.
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| first_indexed | 2025-12-07T18:17:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147861 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:17:49Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
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| spelling | Nowak, A. Stempak, K. Szarek, T.Z. 2019-02-16T09:28:22Z 2019-02-16T09:28:22Z 2016 On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings / A. Nowak, K. Stempak, T.Z. Szarek // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 46 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C99; 42C10; 42C20; 42B20; 42B15; 42B25 DOI:10.3842/SIGMA.2016.096 https://nasplib.isofts.kiev.ua/handle/123456789/147861 We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to Zd2. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, g-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes type. By means of the general Calderón-Zygmund theory we prove that these operators are bounded on weighted Lp spaces, 1 < p < ∞, and from weighted L1 to weighted weak L1. We also obtain similar results for analogous set of operators in the closely related multi-dimensional Laguerre-symmetrized framework. The latter emerges from a symmetrization procedure proposed recently by the first two authors. As a by-product of the main developments we get some new results in the multi-dimensional Laguerre function setting of convolution type. Research of the first-named and the second-named authors was supported by the National Science
 Centre of Poland, project no. 2013/09/B/ST1/02057. The third-named author was partially
 supported by the National Science Centre of Poland, project no. 2012/05/N/ST1/02746. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings Article published earlier |
| spellingShingle | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings Nowak, A. Stempak, K. Szarek, T.Z. |
| title | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings |
| title_full | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings |
| title_fullStr | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings |
| title_full_unstemmed | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings |
| title_short | On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings |
| title_sort | on harmonic analysis operators in laguerre-dunkl and laguerre-symmetrized settings |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147861 |
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