Rafeiro, HumbertoSamko, Stefan2021-09-082021-09-0820210926-2601http://hdl.handle.net/10400.1/17049We introduce generalized local and global Herz spaces where all their characteristics are variable. As one of the main results we show that variable Morrey type spaces and complementary variable Morrey type spaces are included into the scale of these generalized variable Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized variable Herz spaces with application to variable Morrey type spaces and their complementary spaces, based on the mentioned inclusion.engFunction spacesHerz spacesMorrey spaces -and variable exponent spacesSublinear operatorsMaximal functionSingular operatorsMathematicsjournal article10.1007/s11118-020-09891-z