The boundedness of multilinear commutators of Calderón-Zygmund operatorTb→on generalized weighted Morrey spacesMp,φ(w)with the weight functionwbelonging to Muckenhoupt's classApis studied. When1<p<∞andb→=(b1,…,bm),bi∈BMO,i=1,…,m, the sufficient conditions on the pair(φ1,φ2)which ensure the boundedness of the operatorTb→fromMp,φ1(w)toMp,φ2(w)are found. In all cases the conditions for the boundedness ofTb→are given in terms of Zygmund-type integral inequalities on(φ1,φ2), which do not assume any assumption on monotonicity ofφ1(x,r), φ2(x,r)inr.
AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.
In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.
Calderón-Zygmund operators with kernels of Dini's type and their multilinear commutators on generalized variable exponent Morrey spaces
