AI 中文总结
本文研究两类广义加权Morrey空间到广义Morrey空间的连续嵌入，在径向与非径向条件下给出刻画，并证明相关嵌入非紧。
AI 中文摘要
我们研究从两类广义加权Morrey空间到广义Morrey空间的连续嵌入。Komori--Shirai型空间在其规范化中使用立方体的加权测度，而Samko型空间使用Lebesgue测度。我们首先考虑有界域上的广义Morrey空间。在非径向情形下，我们在Morrey函数的局部径向可比较性假设下建立了嵌入结果。作为推论，我们刻画了径向情形下全范围$0<p_1,p_2<\infty$的相应嵌入。然后我们研究与分段幂权函数和一般Muckenhoupt权函数相关的广义Komori--Shirai型加权Morrey空间的嵌入。对于Samko型尺度，我们处理广义和经典加权Morrey空间，同样考虑分段幂权函数和一般Muckenhoupt权函数。最后，假设权函数在某个立方体或球上与正常数可比较，我们证明所考虑的连续嵌入不是紧的。
英文摘要
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 $0<p_1,p_2<\infty$. 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.
CommentsAdded conflict of interest and data availability statements; selected the arXiv.org perpetual, non-exclusive license for v2
