Publication
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces
| dc.contributor.author | Guliyev, Vagif S. | |
| dc.contributor.author | Hasanov, Javanshir J. | |
| dc.contributor.author | Samko, Stefan | |
| dc.date.accessioned | 2018-12-07T14:57:50Z | |
| dc.date.available | 2018-12-07T14:57:50Z | |
| dc.date.issued | 2013-05 | |
| dc.description.abstract | We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r). | |
| dc.description.sponsorship | Science Development Foundation under the President of the Republic of Azerbaijan [EIF-2010-1(1)-40/06-1]; Scientific and Technological Research Council of Turkey (TUBITAK) [110T695] | |
| dc.description.version | info:eu-repo/semantics/publishedVersion | |
| dc.identifier.doi | 10.1016/j.jmaa.2012.03.041 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/11724 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Academic Press Inc Elsevier Science | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Sufficient conditions | |
| dc.subject | Riesz-potentials | |
| dc.subject | Lebesgue spaces | |
| dc.subject | Homogeneous type | |
| dc.subject | Boundedness | |
| dc.subject | L-P(Center-Dot) | |
| dc.title | Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces | |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 84 | |
| oaire.citation.issue | 1 | |
| oaire.citation.startPage | 72 | |
| oaire.citation.title | Journal of Mathematical Analysis and Applications | |
| oaire.citation.volume | 401 | |
| 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 | openAccess | |
| rcaap.type | article | |
| relation.isAuthorOfPublication | 7c853bfc-1d1b-4bd0-9b94-1005fafbd6a4 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7c853bfc-1d1b-4bd0-9b94-1005fafbd6a4 |
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