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 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.United Arab Emirates University, Al Ain, United Arab Emirates [G00002994]; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [19-01-00223, 20-51-46003]; TUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [20-51-46003