Boundedness of the Cesàro averaging operators on Dirichlet spaces
It is shown that the Cesàro averaging operators Cα, Re α > −1, introduced by Stempak, are bounded on the Dirichlet space Da if and only if a > 0, while the associated operators Aα are bounded on Da if and only if −1 < a < 2. This extends results of Galanopoulos, who considered the partic...
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| Published in | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 134; no. 4; pp. 609 - 616 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Edinburgh, UK
Royal Society of Edinburgh Scotland Foundation
01.01.2004
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| Online Access | Get full text |
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| Summary: | It is shown that the Cesàro averaging operators Cα, Re α > −1, introduced by Stempak, are bounded on the Dirichlet space Da if and only if a > 0, while the associated operators Aα are bounded on Da if and only if −1 < a < 2. This extends results of Galanopoulos, who considered the particular case α = 0 for 0 ≤ a ≤ 1. |
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| Bibliography: | PII:S0308210500003371 ArticleID:00337 ark:/67375/6GQ-NXSSB4PN-5 istex:364AF7B4032510BFCC9D25E32FF47AE4BEA9E442 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0308-2105 1473-7124 |
| DOI: | 10.1017/S0308210500003371 |