Weak-type characterizations of Sobolev and bounded variation spaces on metric measure spaces

Tuomas P. Hytönen, Dachun Yang, Wen Yuan +1

Given a complete doubling metric measure space $(X,\rho ,\mu )$ supporting a Poincaré inequality, we prove weak-type characterizations of the Sobolev space ${\dot{W}}^{1,p}(\mu )$ and the spac…