Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator
We consider the generalized shift operator, associated with the Dunkl operator Λα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2), α>-1/2. We study some embeddings into the Morrey space (D-Morrey space) Lp,λ,α, 0≤λ<2α+2 and modified Morrey space (modified D-Morrey space) L̃p,λ,α associated with th...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/291345 |
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| author | Emin V. Guliyev Yagub Y. Mammadov |
| author_facet | Emin V. Guliyev Yagub Y. Mammadov |
| author_sort | Emin V. Guliyev |
| collection | DOAJ |
| description | We consider the generalized shift operator, associated with the Dunkl operator Λα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2), α>-1/2. We study some embeddings into the Morrey space (D-Morrey space) Lp,λ,α, 0≤λ<2α+2 and modified Morrey space (modified D-Morrey space) L̃p,λ,α associated with the Dunkl operator on ℝ. As applications we get boundedness of the fractional maximal operator Mβ, 0≤β<2α+2, associated with the Dunkl operator (fractional D-maximal operator) from the spaces Lp,λ,α to L∞(ℝ) for p=(2α+2-λ)/β and from the spaces L̃p,λ,α(ℝ) to L∞(ℝ) for (2α+2-λ)/β≤p≤(2α+2)/β. |
| format | Article |
| id | doaj-art-8dccb665090042699af7cdd8fae385b3 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8dccb665090042699af7cdd8fae385b32025-08-20T02:09:41ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/291345291345Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl OperatorEmin V. Guliyev0Yagub Y. Mammadov1Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, AzerbaijanInstitute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, AzerbaijanWe consider the generalized shift operator, associated with the Dunkl operator Λα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2), α>-1/2. We study some embeddings into the Morrey space (D-Morrey space) Lp,λ,α, 0≤λ<2α+2 and modified Morrey space (modified D-Morrey space) L̃p,λ,α associated with the Dunkl operator on ℝ. As applications we get boundedness of the fractional maximal operator Mβ, 0≤β<2α+2, associated with the Dunkl operator (fractional D-maximal operator) from the spaces Lp,λ,α to L∞(ℝ) for p=(2α+2-λ)/β and from the spaces L̃p,λ,α(ℝ) to L∞(ℝ) for (2α+2-λ)/β≤p≤(2α+2)/β.http://dx.doi.org/10.1155/2010/291345 |
| spellingShingle | Emin V. Guliyev Yagub Y. Mammadov Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator Abstract and Applied Analysis |
| title | Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator |
| title_full | Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator |
| title_fullStr | Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator |
| title_full_unstemmed | Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator |
| title_short | Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator |
| title_sort | some embeddings into the morrey and modified morrey spaces associated with the dunkl operator |
| url | http://dx.doi.org/10.1155/2010/291345 |
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