Convolution Algebraic Structures Defined by Hardy-Type Operators
The main aim of this paper is to show that certain Banach spaces, defined via integral kernel operators, are Banach modules (with respect to some known Banach algebras and convolution products on ℝ+). To do this, we consider some suitable kernels such that the Hardy-type operator is bounded in weigh...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/212465 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548505386745856 |
|---|---|
| author | Pedro J. Miana Juan J. Royo Luis Sánchez-Lajusticia |
| author_facet | Pedro J. Miana Juan J. Royo Luis Sánchez-Lajusticia |
| author_sort | Pedro J. Miana |
| collection | DOAJ |
| description | The main aim of this paper is to show that certain Banach spaces, defined via integral kernel operators, are Banach modules (with respect to some known Banach algebras and convolution products on ℝ+). To do this, we consider some suitable kernels such that the Hardy-type operator is bounded in weighted Lebesgue spaces Lωpℝ+ for p≥1. We also show new inequalities in these weighted Lebesgue spaces. These results are applied to several concrete function spaces, for example, weighted Sobolev spaces and fractional Sobolev spaces defined by Weyl fractional derivation. |
| format | Article |
| id | doaj-art-ece86f98e87d47b48f129a4d6781a91e |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-ece86f98e87d47b48f129a4d6781a91e2025-02-03T06:13:58ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/212465212465Convolution Algebraic Structures Defined by Hardy-Type OperatorsPedro J. Miana0Juan J. Royo1Luis Sánchez-Lajusticia2Departamento de Matemáticas e IUMA, Universidad de Zaragoza, 50009 Zaragoza, SpainDepartamento de Matemáticas e IUMA, Universidad de Zaragoza, 50009 Zaragoza, SpainDepartamento de Matemáticas e IUMA, Universidad de Zaragoza, 50009 Zaragoza, SpainThe main aim of this paper is to show that certain Banach spaces, defined via integral kernel operators, are Banach modules (with respect to some known Banach algebras and convolution products on ℝ+). To do this, we consider some suitable kernels such that the Hardy-type operator is bounded in weighted Lebesgue spaces Lωpℝ+ for p≥1. We also show new inequalities in these weighted Lebesgue spaces. These results are applied to several concrete function spaces, for example, weighted Sobolev spaces and fractional Sobolev spaces defined by Weyl fractional derivation.http://dx.doi.org/10.1155/2013/212465 |
| spellingShingle | Pedro J. Miana Juan J. Royo Luis Sánchez-Lajusticia Convolution Algebraic Structures Defined by Hardy-Type Operators Journal of Function Spaces and Applications |
| title | Convolution Algebraic Structures Defined by Hardy-Type Operators |
| title_full | Convolution Algebraic Structures Defined by Hardy-Type Operators |
| title_fullStr | Convolution Algebraic Structures Defined by Hardy-Type Operators |
| title_full_unstemmed | Convolution Algebraic Structures Defined by Hardy-Type Operators |
| title_short | Convolution Algebraic Structures Defined by Hardy-Type Operators |
| title_sort | convolution algebraic structures defined by hardy type operators |
| url | http://dx.doi.org/10.1155/2013/212465 |
| work_keys_str_mv | AT pedrojmiana convolutionalgebraicstructuresdefinedbyhardytypeoperators AT juanjroyo convolutionalgebraicstructuresdefinedbyhardytypeoperators AT luissanchezlajusticia convolutionalgebraicstructuresdefinedbyhardytypeoperators |