Rafeiro, HumbertoSamko, Stefan2021-09-082021-09-082021-072662-2033http://hdl.handle.net/10400.1/16952We study embeddings of Morrey type spaces M-p,M-q,M-omega(R-n), 1 <= p < infinity, 1 <= q < infinity, both local and global, into weighted Lebesgue spaces L-p(R-n, w), with the main goal to better understand the local behavior of functions f is an element of M-p,M-q,M-omega(R-n) and also their behavior at infinity. Under some assumptions on the function omega, we prove that the local Morrey type space is embedded into L-p(R-n, w), where w(r) = omega(r) if q = 1, and w(r) is "slightly distorted" in comparison with omega(r) if q > 1. In the case q > p we show that the embedding, in general, cannot hold with omega = w. For global Morrey type spaces we also prove embeddings into Stummel spaces. Similar embeddings for complementary Morrey type spaces are obtained. We also study inverse embeddings of weighted Lebesgue spaces L-p(R-n, w) into Morrey type and complementary Morrey type spaces. Finally, using our previous results on relations between Herz and Morrey type spaces, we obtain "for free" similar embeddings for Herz spaces.engMorrey type spacesWeighted Lebesgue spacesEmbeddingsStummel spacesHerz spacesMathematicsjournal article10.1007/s43037-021-00128-8