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

Rafeiro, H.; Samko, Stefan G.

http://hdl.handle.net/10400.1/16968

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Authors

Rafeiro, H.

Samko, Stefan G.

Abstract(s)

For a class of sublinear operators, we find conditions on the variable exponent Morrey-type space L-p(.),L-q,L-omega(.,L-.)(R-n) ensuring the boundedness in this space. A priori assumptions on this class are that the operators are bounded in L-p(.)(R-n) and satisfy some size condition. This class includes in particular the maximal operator, singular operators with the standard kernel, and the Hardy operators. Wealso prove embedding of variable exponent Morrey-type spaces into weighted L-p(.)-spaces.