Reverse Carleson inequalities for weighted Fock spaces with $A_{\infty }$-type weights

Abstract

We characterize dominating sets for weighted Fock spaces $F_{\hat{I}\pm ,w}^p$ induced by Muckenhoupt $A_{\infty }$ weights, which leads to a sufficient condition for reverse Carleson measures for the spaces $F_{\hat{I}\pm ,w}^p$ with restricted $A_{\infty }$ weights. Applications to invertibility of Toeplitz operators, closed range property of Volterra operators, and atomic decomposition of $F_{\hat{I}\pm ,w}^p$ are given.