Poincaré inequalities and $A_p$ weights on bow-ties

Anders Björn, Jana Björn, Andreas Christensen

A metric space $X$ is called a \emph{bow-tie} if it can be written as $X=X_{+}\cup X_{-}$, where $X_{+}\cap X_{-}=\{x_0\}$ and $X_{\pm }\ne \{x_0\}$ are closed subsets of $X$. We…