论文标题
准空间，Lipschitz和BV映射
Quasiconformal, Lipschitz, and BV mappings in metric spaces
论文作者
论文摘要
考虑两个公制度量空间之间的映射$ f \ colon x \ y $。我们研究了本地Lipschitz编号$ \ MATHRM {LIP} F $的广义版本，以及用于定义Quasiconformal映射的失真号$ H_F $。使用这些，我们给出了足够的条件，以$ f $为bv映射$ f \ bv _ {\ mathrm {loc}}}（x; y）$或newton-sobolev映射$ f \ in n _ {\ mathrm {loc mathrm {loc}}}}}}}}^{1，p}（x; y）$ p <
Consider a mapping $f\colon X\to Y$ between two metric measure spaces. We study generalized versions of the local Lipschitz number $\mathrm{Lip} f$, as well as of the distortion number $H_f$ that is used to define quasiconformal mappings. Using these, we give sufficient conditions for $f$ being a BV mapping $f\in BV_{\mathrm{loc}}(X;Y)$ or a Newton-Sobolev mapping $f\in N_{\mathrm{loc}}^{1,p}(X;Y)$, with $1\le p<\infty$.
