Embeddings of Generalized Weighted Morrey Spaces
Abstract
We study continuous embeddings from two classes of generalized weighted Morrey spaces into generalized Morrey spaces. The Komori--Shirai-type spaces use the weighted measure of cubes in their normalization, whereas the Samko-type spaces use the Lebesgue measure. We first consider generalized Morrey spaces on bounded domains. In the non-radial setting, we establish embedding results under local radial comparability assumptions on the Morrey functions. As a consequence, we characterize the corresponding embeddings in the radial setting for the full range 0<p1,p2<∞. We then study embeddings from generalized Komori--Shirai-type weighted Morrey spaces associated with piecewise power weights and general Muckenhoupt weights. For the Samko-type scale, we treat both generalized and classical weighted Morrey spaces, again considering piecewise power weights and general Muckenhoupt weights. Finally, assuming that the weight is comparable to a positive constant on some cube or ball, we show that the continuous embeddings under consideration are not compact.
Related
- Optimal Embeddings of Campanato and Morrey Spaces
- Derivative Embeddings in Vector-Valued Morrey Spaces
- Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators
- Compact Embeddings of Vector-Valued Morrey Spaces
- Commutators of a class of Ψ-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications
BibTeX
@misc{liu2026embeddings,
title = {{Embeddings of Generalized Weighted Morrey Spaces}},
author = {Zhen Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09241},
eprint = {2610.09241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09241},
}
RIS
TY - UNPB
TI - Embeddings of Generalized Weighted Morrey Spaces
AU - Zhen Liu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.09241
UR - https://arxiv.org/abs/2610.09241
AB - We study continuous embeddings from two classes of generalized weighted Morrey spaces into generalized Morrey spaces. The Komori--Shirai-type spaces use the weighted measure of cubes in their normalization, whereas the Samko-type spaces use the Lebesgue measure. We first consider generalized Morrey spaces on bounded domains. In the non-radial setting, we establish embedding results under local radial comparability assumptions on the Morrey functions. As a consequence, we characterize the corresponding embeddings in the radial setting for the full range 0<p_1,p_2<∞. We then study embeddings from generalized Komori--Shirai-type weighted Morrey spaces associated with piecewise power weights and general Muckenhoupt weights. For the Samko-type scale, we treat both generalized and classical weighted Morrey spaces, again considering piecewise power weights and general Muckenhoupt weights. Finally, assuming that the weight is comparable to a positive constant on some cube or ball, we show that the continuous embeddings under consideration are not compact.
ER -