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In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.
In the paper we find conditions on the pair which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space to another , , and from the space to the weak space . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.
In this paper, characterizations of the embeddings between weighted Copson function spaces and weighted Cesàro function spaces are given. In particular, two-sided estimates of the optimal constant in the inequality
where , and , , , are weights on , are obtained. The most innovative part consists of the fact that possibly different parameters and and possibly different inner weights and are allowed. The proof is based on the combination of duality techniques with estimates...
In this paper, the boundedness of a large class of sublinear commutator operators generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces with the weight function belonging to Muckenhoupt’s class is studied. When and , sufficient conditions on the pair which ensure the boundedness of the operator from to are found. In all cases the conditions for the boundedness of are given in terms of Zygmund-type integral inequalities on , which do not require...
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