Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces
Yazarlar (4)
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Azerbaijan National Academy Of Sciences, Azerbaycan
Dr. Öğr. Üyesi Turhan KARAMAN
Kırşehir Ahi Evran Üniversitesi, Türkiye
Azerbaijan National Academy Of Sciences, Azerbaycan
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Integral Equations and Operator Theory (Q4) | ||
| Dergi ISSN | 0378-620X Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SSCI | ||
| Makale Dili | İngilizce | Basım Tarihi | 11-2011 |
| Cilt / Sayı / Sayfa | 71 / 3 / 327–355 | DOI | 10.1007/s00020-011-1904-1 |
| Özet |
| In this paper the authors study the boundedness for a large class of sublinear operators Tα,α ∈ [0, n) generated by Calderón-Zygmund operators (α = 0) and generated by Riesz potential operator (α > 0) on generalized Morrey spaces Mp,φ. As an application of the above result, the boundeness of the commutator of sublinear operators Tb,α, α ∈ [0, n) on generalized Morrey spaces is also obtained. In the case b ∈ BMO and Tb,α is a sublinear operator, we find the sufficient conditions on the pair (φ1, φ2) which ensures the boundedness of the operators Tb,α, α ∈ [0, n) from one generalized Morrey space Mp,φ1 to another Mq,φ2 with 1/p - 1/q = α/n. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on (φ1, φ2), which do not assume any assumption on monotonicity of φ1, φ2 in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator. © 2011 Springer Basel AG. |
| Anahtar Kelimeler |
| BMO | Bochner-Riesz operator | Calderón-Zygmund operator | commutator | fractional maximal operator | generalized Morrey space | Littlewood-Paley operator | Marcinkiewicz operator | Riesz potential operator | Sublinear operator |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| WoS | 95 |
| SCOPUS | 96 |