ROUGH SINGULAR INTEGRAL OPERATORS AND ITS COMMUTATORS ON GENERALIZED WEIGHTED MORREY SPACES
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Nakhchivan Teachers Institute, Azerbaycan
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Mathematical Inequalities and Applications (Q1) | ||
| Dergi ISSN | 1331-4343 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 07-2016 |
| Cilt / Sayı / Sayfa | 19 / 3 / 863–881 | DOI | 10.7153/mia-19-63 |
| Özet |
| Let Omega is an element of L-q(Sn-1) be a homogeneous function of degree zero with q > 1 and have a mean value zero on Sn-1. In this paper, we study the boundedness of the singular integral operators with rough kernels T-Omega and their commutators [b, T-Omega] on generalized weighted Morrey spaces M-p,M-phi(w). We find the sufficient conditions on the pair (phi(1), phi(2)) with q' <= p < infinity, p not equal 1 and w is an element of A(p/q') or 1 < p < q and w(1-p') is an element of A(p'/q') which ensures the boundedness of the operators T-Omega from one generalized weighted Morrey space M-p,M-phi 1 (w) to another M-p,M-phi 2(w) for 1 < p < infinity. We find the sufficient conditions on the pair (phi(1), phi(2)) with b is an element of BMO(R-n) and q' <= p < infinity, p not equal 1, w is an element of A(p/q') or 1 < p < q, w(1-p'). A(p'/q') which ensures the boundedness of the operators [b, T-Omega] from M-p,M-phi 1(w) to M-p,M-phi 2 (w) for 1 < p < infinity. In all cases the conditions for the boundedness of the operators T-Omega, [b, T-Omega] are given in terms of Zygmund-type integral inequalities on (phi(1), phi(2)) and w, which do not assume any assumption on monotonicity of phi(1)(x, r), phi(2)(x, r) in r. |
| Anahtar Kelimeler |
| Ap Weights | Commutator | Generalized Weighted Morrey Spaces | Ingular integral Operator | Rough Kernel |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| WoS | 7 |
| SCOPUS | 12 |
| Google Scholar | 17 |