Rafeiro, HumbertoSamko, Stefan2021-06-242021-06-242020-09-141069-5869http://hdl.handle.net/10400.1/16391We introduce local and global generalized Herz spaces. As one of the main results we show that Morrey type spaces and complementary Morrey type spaces are included into the scale of these Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized Herz spaces with application to Morrey type spaces and their complementary spaces, based on the mentioned inclusion.engFunction spacesHerz spacesMorrey type spacesSublinear operatorsMaximal functionSingular operatorsMathematicsjournal article10.1007/s00041-020-09778-y