Toeplitz operators and Carleson measure between weighted Bergman spaces induced by regular weights

Abstract: In this paper, we give a universal description of the boundedness and compactness of Toeplitz operator $\mathcal{T}\mu^\omega$ between Bergman spaces $A\eta^p$ and $A_\upsilon^q$ when $\mu$ is a positive Borel measure, $1<p,q<\infty$ and $\omega,\eta,\upsilon$ are regular weights. By using Khinchin's inequality and Kahane's inequality, we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.