AI 中文总结
该研究针对加权局部Morrey型与互补局部Morrey型空间，通过一维归约方法结合Cesàro和Copson空间嵌入刻画的最新结果，给出两类空间间连续嵌入的充要条件，覆盖所有有限参数情形。
AI 中文摘要
本文建立了加权局部Morrey型空间与加权互补局部Morrey型空间之间连续嵌入的充要条件。我们的方法不依赖标准的多维方法，而是基于一维归约，具体而言，将多维嵌入问题归约为涉及一维Cesàro和Copson函数空间的相应加权不等式。结合该归约与Cesàro和Copson空间之间嵌入刻画的最新结果，我们给出了嵌入LM_{p1,q1}(v1,w1) ↪ LM_{p2,q2}(v2,w2)及对偶LM_{p1,q1}(v1,w1) ↪ LM_{p2,q2}(v2,w2)的完整刻画，结果覆盖参数0 < p1,p2,q1,q2 < ∞的所有有限情形。
英文摘要
In this paper, we establish necessary and sufficient conditions for continuous embeddings between weighted local Morrey-type spaces and weighted complementary local Morrey-type spaces. Rather than relying on standard multidimensional approaches, our methodology is based on a one-dimensional reduction. Specifically, we reduce the multidimensional embedding problems to corresponding weighted inequalities involving one-dimensional Cesàro and Copson function spaces. Applying this reduction alongside recent results in the characterization of the embeddings between Cesàro and Copson spaces, we provide complete characterizations for the embeddings \[ \LM_{p_1,q_1}(v_1, w_1) \hookrightarrow \LM_{p_2,q_2}(v_2, w_2)\] and \[\dual\LM_{p_1,q_1}(v_1, w_1) \hookrightarrow \LM_{p_2,q_2}(v_2, w_2).\] Our results cover all possible finite cases of the parameters $0 < p_1, p_2, q_1, q_2 < \infty$.
Comments19 pages
