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...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147861 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147861 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1478612019-02-17T01:23:16Z On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings Nowak, A. Stempak, K. Szarek, T.Z. 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. 2016 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Nowak, A. Stempak, K. Szarek, T.Z. |
| spellingShingle |
Nowak, A. Stempak, K. Szarek, T.Z. On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Nowak, A. Stempak, K. Szarek, T.Z. |
| author_sort |
Nowak, A. |
| title |
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_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_sort |
on harmonic analysis operators in laguerre-dunkl and laguerre-symmetrized settings |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147861 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT nowaka onharmonicanalysisoperatorsinlaguerredunklandlaguerresymmetrizedsettings AT stempakk onharmonicanalysisoperatorsinlaguerredunklandlaguerresymmetrizedsettings AT szarektz onharmonicanalysisoperatorsinlaguerredunklandlaguerresymmetrizedsettings |
| first_indexed |
2023-05-20T17:28:42Z |
| last_indexed |
2023-05-20T17:28:42Z |
| _version_ |
1796153391318040576 |