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

For a class of sublinear operators, we find conditions on the variable exponent Morrey-type space (Formula presented.) ensuring the boundedness in this space. A priori assumptions on this class are that the operators are bounded in (Formula presented.) and 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 (Formula presented.) -spaces.