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For a class of sublinear operators, we find conditions on the variable exponent Morrey-type spaceensuring the boundedness in this space. A priori assumptions on this class are that the operators are bounded inand satisfy some size condition. This class includes in particular the maximal operator, singular operators with the standard kernel, and the Hardy operators. We also prove embedding of variable exponent Morrey-type spaces into weighted-spaces.

On a class of sublinear operators in variable exponent Morrey-type spaces