ROUGH SINGULAR INTEGRAL OPERATORS AND ITS COMMUTATORS ON GENERALIZED WEIGHTED MORREY SPACES
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
Vugar H. Hamzayev
Nakhchivan Teachers Institute, Azerbaycan
Nakhchivan Teachers Institute, Azerbaycan
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
|
||
| 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 |
| Makale Linki | https://files.ele-math.com/articles/mia-19-63.pdf | ||
| Özet |
| Let Ω∈ Lq (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 TΩ and their commutators [b, TΩ] on generalized weighted Morrey spaces Mp, ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with q≤ p<∞, p= 1 and w∈ Ap/q or 1< p< q and w1− p∈ Ap/q which ensures the boundedness of the operators TΩ from one generalized weighted Morrey space Mp, ϕ1 (w) to another Mp, ϕ2 (w) for 1< p<∞. We find the sufficient conditions on the pair (ϕ1, ϕ2) with b∈ BMO (Rn) and q≤ p<∞, p= 1, w∈ Ap/q or 1< p< q, w1− p∈ Ap/q which ensures the boundedness of the operators [b, TΩ] from Mp, ϕ1 (w) to Mp, ϕ2 (w) for 1< p<∞. In all cases the conditions for the boundedness of the operators TΩ,[b, TΩ] are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2) and w, which do not assume any assumption on monotonicity of ϕ1 (x, r), ϕ2 (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 |