带局部权重的庞加莱-索伯列夫不等式的推广
Generalization for Poincaré--Sobolev inequalities with local weights
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中文总结 AI 辅助
本文研究了不假设Muckenhoupt条件时，依赖区域立方体的局部权重下庞加莱-索伯列夫不等式的加权推广，并将其应用于齐次与非齐次型索伯列夫嵌入定理的加权推广。
中文摘要 AI 辅助
众所周知，在每个区域立方体（或球）上存在称为庞加莱-索伯列夫不等式的局部积分不等式。此后，众多学者研究了该不等式在Muckenhoupt型权重或与区域立方体无关的全局权重下的推广。本文中，我们在不假设Muckenhoupt条件的情况下，研究了该不等式在依赖于区域立方体的局部权重下的类似加权推广；此外，作为应用，我们还考虑了齐次和非齐次型索伯列夫嵌入定理的加权推广。
英文摘要
It is well known the local integral inequality which is called Poincaré--Sobolev inequality on each domain cube (or ball). After that many authors investigated the generalization for this inequality with Muckenhoupt-type weights or global weights which are independent of the domain cube. In this paper, we investigated similar weighted generalization for this inequality with the local weights which are depending on the domain cube without assuming the Muckenhoupt condition. Moreover, we considered the weighted generalization for the homogeneous and inhomogeneous-type Sobolev embedding theorems as some applications.
