Toeplitz and Hankel operators on Bergman spaces with doubling weights

In this paper, we focus on the boundedness and compactness of the Toeplitz operators and the Hankel operators on the $\mathcal{D}$-weighted Bergman spaces $A_ω^p$ ($1\leq p<\infty$). In particular, the boundedness of Toeplitz operators with $\mathrm{BMO}_ω^p$-symbols on $A_ω^p$ is characterized in t