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

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, $1<p,q<\mathrm{\infty }$ 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.