| Yazarlar |
Seymur S. Aliev
|
Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi |
| Özet |
| In this paper we study the boundedness of the parametric Marcinkiewicz operator mu(rho)(Omega) on generalized Morrey spaces M-p,M-phi. We find the sufficient conditions on the pair (phi(1), phi(2)) which ensure the boundedness of the operators mu(rho)(Omega) from one generalized Morrey space A to another M-p,M-phi 2, 1 < p < infinity, and from the space M-1,M-phi 1 to the weak space WM1,phi 2. As an application of the above result, the boundedness of the commutator of Marcinkiewicz operators [a, mu(rho)(Omega)] on generalized Morrey spaces is also obtained. In the case a is an element of BMO(R-n), we find the sufficient conditions on the pair (phi(1), phi(2)) which ensure the boundedness of the operators [a, mu(rho)(Omega)] from one generalized Morrey space M-p,M-phi 1 to another M-p,M-phi 2 1 < p < infinity, and from the space M-1,M-phi 1 to the weak space WM1,phi 2. In all the cases the conditions for boundedness are given in terms of Zygmund-type integral inequalities on (phi(1), phi(2)) which do not require any assumption on the monotonicity of phi(1), phi(2). |
| Anahtar Kelimeler |
| BMO | Commutator | Generalized Morrey space | Parametric Marcinkiewicz operator |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale |
| Dergi Adı | GEORGIAN MATHEMATICAL JOURNAL |
| Dergi ISSN | 1072-947X |
| Dergi Grubu | Q4 |
| Makale Dili | İngilizce |
| Basım Tarihi | 01-2012 |
| Cilt No | 19 |
| Sayı | 2 |
| Sayfalar | 195 / 208 |
| Doi Numarası | 10.1515/gmj-2012-0008 |
| Atıf Sayıları | |
| WoS | 16 |
| SCOPUS | 18 |
| Google Scholar | 26 |
