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COMMUTATORS OF MARCINKIEWICZ INTEGRALS ASSOCIATED WITH SCHRODINGER OPERATOR ON GENERALIZED WEIGHTED MORREY SPACES   
Yazarlar
 Vagıf GULIYEV Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi
 Ali AKBULUT Ali AKBULUT
Kırşehir Ahi Evran Üniversitesi
Vugar H. Hamzayev
 Okan KUZU Okan KUZU
Kırşehir Ahi Evran Üniversitesi
Özet
Let L = -Delta + V be a Schrodinger operator, where Delta is the Laplacian on R-n, while nonnegative potential V belongs to the reverse Holder class. Let also 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 Marcinkiewicz operators mu(L)(j,Omega) and their commutators mu(L)(j,Omega,b) with rough kernels associated with Schrodinger operator 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 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 mu(L)(j,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, w is an element of A(p/q') or 1 < p < q w(1-p') is an element of A(p'/q') which ensures the boundedness of the operators mu(L)(j,Omega,b), j = 1, ... , n 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 mu(L)(j,Omega), mu(L)(j,Omega,b), j = 1, ... , n 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
Commutator, Ap weights | Generalized weighted Morrey spaces | Marcinkiewicz operator | Rough kernel | Schrödinger operator
Makale Türü Özgün Makale
Makale Alt Türü SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale
Dergi Adı JOURNAL OF MATHEMATICAL INEQUALITIES
Dergi ISSN 1846-579X
Dergi Grubu Q1
Makale Dili İngilizce
Basım Tarihi 12-2016
Cilt No 10
Sayı 4
Sayfalar 947 / 970
Doi Numarası 10.7153/jmi-10-77