Absolutely continuous mappings on doubling metric measure spaces
Absolutely continuous mappings on doubling metric measure spaces
复制标题
加倍度量测度空间上的绝对连续映射
DOI：
10.1007/s00229-023-01460-z
复制
发表时间：
2023
影响因子：
0.6
通讯作者：
Zhou Xiaodan
中科院分区：
文献类型：
--
作者：
Lahti Panu;Zhou Xiaodan
我们考虑加倍度量测度空间X和Banach空间V之间的Q-绝对连续映射。研究了这些映射与 Sobolev 映射之间的关系。特别是，AhlforsQ-正则空间上的局部 Q-绝对连续映射是连续映射，并且在 Cheeger 导数方面几乎处处可微，前提是 V 满足 Radon-Nikodym 性质。相反，虽然连续 Sobolev 映射通常不是局部 Q 绝对连续的，但当且仅当进一步假定为伪单调时，该含义成立。由此可见，满足松弛拟共形条件的伪单调映射也是 Q 绝对连续的。
We considerQ-absolutely continuous mappingsbetween a doubling metric measure spaceXand a Banach spaceV. The relation between these mappings and Sobolev mappingsforis investigated. In particular, a locallyQ-absolutely continuous mapping on an AhlforsQ-regular space is a continuous mapping in, as well as differentiable almost everywhere in terms of Cheeger derivatives providedVsatisfies the Radon-Nikodym property. Conversely, though a continuous Sobolev mappingis generally not locallyQ-absolutely continuous, this implication holds iffis further assumed to be pseudomonotone. It follows that pseudomonotone mappings satisfying a relaxed quasiconformality condition are alsoQ-absolutely continuous.