Differences of the weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces

Abstract

We characterize the boundedness and compactness of the differences of weighted differentiation composition operators $D^n_{\varphi_1, u_1} - D^n_{\varphi_2, u_2}$, where $n \in N_0, u_1, u_2 \in H(D)$, and $\varphi_1, \varphi_2 \in S(D)$, from mixed-norm spaces $H(p, q, \phi)$, where $0 < p,\; q < \infty$ and \phi is normal, to weighted-type spaces $H^{\infty}_v$.