COMMUTATORS OF MARCINKIEWICZ INTEGRALS ASSOCIATED WITH SCHRODINGER OPERATOR ON GENERALIZED WEIGHTED MORREY SPACES
Yazarlar (4)
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
Prof. Dr. Ali AKBULUT Kırşehir Ahi Evran Üniversitesi, Türkiye
Vugar H. Hamzayev
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Doç. Dr. Okan KUZU Kırşehir Ahi Evran Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
|
||
| Dergi Adı | Journal of Mathematical Inequalities (Q1) | ||
| Dergi ISSN | 1846-579X Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 12-2016 |
| Cilt / Sayı / Sayfa | 10 / 4 / 947–970 | DOI | 10.7153/jmi-10-77 |
| Makale Linki | https://www.academia.edu/download/72520040/22190ec422a29b7dc3572b5715792735eb06.pdf | ||
| Özet |
| Let L=− Δ+ V be a Schrödinger operator, where Δ is the Laplacian on Rn, while nonnegative potential V belongs to the reverse Hölder class. Let also 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 Marcinkiewicz operators µL j, Ω and their commutators µL j, Ω, b with rough kernels associated with Schrödinger operator on generalized weighted Morrey spaces Mp, ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with q′< p<∞ and w∈ Ap/q′ or 1< p< q and w1− p′∈ Ap′/q′ which ensures the boundedness of the operators µL j, Ω 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<∞, w∈ Ap/q′ or1< p< q, w1− p′∈ Ap′/q′ which ensures the boundedness of the operators µL j, Ω, b, j= 1,..., n from Mp, ϕ1 (w) to Mp, ϕ2 (w) for 1< p<∞. In all cases the conditions for the boundedness of the operators µL j, Ω, µL j, Ω, b, j= 1,..., n 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 |
| Commutator, Ap weights | Generalized weighted Morrey spaces | Marcinkiewicz operator | Rough kernel | Schrödinger operator |
