On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
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| Creator |
Nowak, A.
Stempak, K. Szarek, T.Z. |
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| 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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| Date |
2019-02-16T09:28:22Z
2019-02-16T09:28:22Z 2016 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/147861 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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