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On Grand Lebesgue spaces on sets of infinite measure
| dc.contributor.author | Samko, Stefan | |
| dc.contributor.author | Umarkhadzhiev, Salaudin | |
| dc.date.accessioned | 2019-11-20T15:07:43Z | |
| dc.date.available | 2019-11-20T15:07:43Z | |
| dc.date.issued | 2017-04 | |
| dc.description.abstract | We consider grand Lebesgue spaces on sets of infinite measure and study the dependence of these spaces on the choice of the so-called. We also consider Mikhlin and Marcinkiewicz theorems on Fourier multipliers in the setting of grand spaces. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim | |
| dc.description.abstract | The theory of grand spaces is intensively developed during the last two decades. Such spaces L p)(), 1 < p < ∞, on bounded sets ⊂ Rn were introduced by T. Iwaniec and C. Sbordone [8] in connection with application to differential equations. In the last years, operators of harmonic analysis were widely studied in such spaces, see [1]–[6], [11]–[15] and the references therein. Some of these results are presented in the books [16], [17]. In all the above mentioned studies only sets of finite measure were allowed, based on the embedding L p ⊂ L p−ε. In the papers [23], [24], [26] there was suggested an approach to define grand spaces L p) a () on sets ⊆ Rn of not necessarily finite measure. In the general form given in [26], this approach is based on introducing the small power aε of a weight a into the norm of grand space, see (2.1). We call this function a, which determines the grand space L p) a (), the of this space. | |
| dc.description.sponsorship | Russian Fund for Basic Research [15-01-02732] | |
| dc.description.version | info:eu-repo/semantics/publishedVersion | |
| dc.identifier.doi | 10.1002/mana.201600136 | |
| dc.identifier.issn | 0025-584X | |
| dc.identifier.issn | 1522-2616 | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/13177 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Wiley-V C H Verlag Gmbh | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Lp spaces | |
| dc.title | On Grand Lebesgue spaces on sets of infinite measure | |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 919 | |
| oaire.citation.issue | 05-jun | |
| oaire.citation.startPage | 913 | |
| oaire.citation.title | Mathematische Nachrichten | |
| oaire.citation.volume | 290 | |
| 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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