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dc.contributor.author |
Nowak, A. |
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dc.contributor.author |
Stempak, K. |
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dc.contributor.author |
Szarek, T.Z. |
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dc.date.accessioned |
2019-02-16T09:28:22Z |
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dc.date.available |
2019-02-16T09:28:22Z |
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dc.date.issued |
2016 |
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dc.identifier.citation |
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. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 42C99; 42C10; 42C20; 42B20; 42B15; 42B25 |
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dc.identifier.other |
DOI:10.3842/SIGMA.2016.096 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/147861 |
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dc.description.abstract |
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. |
uk_UA |
dc.description.sponsorship |
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. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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