Publication
Hadamard-Bergman Convolution Operators
| dc.contributor.author | Karapetyants, Alexey | |
| dc.contributor.author | Samko, Stefan | |
| dc.date.accessioned | 2021-06-24T11:35:10Z | |
| dc.date.available | 2021-06-24T11:35:10Z | |
| dc.date.issued | 2020-10 | |
| dc.description.abstract | We introduce a convolution form, in terms of integration over the unit disc D, for operators on functions f in H(D), which correspond to Taylor expansion multipliers. We demonstrate advantages of the introduced integral representation in the study of mapping properties of such operators. In particular, we prove the Young theorem for Bergman spaces in terms of integrability of the kernel of the convolution. This enables us to refer to the introduced convolutions as Hadamard-Bergman convolution. Another, more important, advantage is the study of mapping properties of a class of such operators in Holder type spaces of holomorphic functions, which in fact is hardly possible when the operator is defined just in terms of multipliers. Moreover, we show that for a class of fractional integral operators such a mapping between Holder spaces is onto. We pay a special attention to explicit integral representation of fractional integration and differentiation. | |
| dc.description.sponsorship | Russian Foundation for Fundamental ResearchRussian Foundation for Basic Research (RFBR) [18-01-00094-a] | |
| dc.description.sponsorship | Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [18-01-00094-a, 19-01-00223-a] | |
| dc.description.version | info:eu-repo/semantics/publishedVersion | |
| dc.identifier.doi | 10.1007/s11785-020-01035-w | |
| dc.identifier.issn | 1661-8254 | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/16362 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Springer | |
| dc.subject | Hadamard-Bergman convolution operators | |
| dc.subject | Holder space of holomorphic functions | |
| dc.subject | Fractional integro-differentiation | |
| dc.subject | 47G10 | |
| dc.subject | 47B38 | |
| dc.subject | 46E30 | |
| dc.subject.other | Mathematics | |
| dc.title | Hadamard-Bergman Convolution Operators | |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.issue | 8 | |
| oaire.citation.startPage | 77 | |
| oaire.citation.title | Complex Analysis and Operator Theory | |
| oaire.citation.volume | 14 | |
| person.familyName | Samko | |
| person.givenName | Stefan | |
| person.identifier.orcid | 0000-0002-8022-2863 | |
| person.identifier.rid | M-3726-2013 | |
| person.identifier.scopus-author-id | 6603416048 | |
| rcaap.rights | restrictedAccess | |
| rcaap.type | article | |
| relation.isAuthorOfPublication | 7c853bfc-1d1b-4bd0-9b94-1005fafbd6a4 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7c853bfc-1d1b-4bd0-9b94-1005fafbd6a4 |
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