Abstract
Abstract Consider a mapping f : X → Y {f\colon X\to Y} between two metric measure spaces. We study generalized versions of the local Lipschitz number Lip f {\operatorname{Lip}f} , as well as of the distortion number H f {H_{f}} that is used to define quasiconformal mappings. Using these numbers, we give sufficient conditions for f being a BV mapping f ∈ BV loc ( X ; Y ) {f\in\mathrm{BV}_{\mathrm{loc}}(X;Y)} or a Newton–Sobolev mapping f ∈ N loc 1 , p ( X ; Y ) {f\in N_{\mathrm{loc}}^{1,p}(X;Y)} , with 1 ≤ p < ∞ {1\leq p<\infty} .
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