Differences of weighted composition operators from Hardy space to weighted-type spaces on the unit ball

summary:In this paper, we limit our analysis to the difference of the weighted composition operators acting from the Hardy space to weighted-type space in the unit ball of $\mathbb {C}^N$, and give some necessary and sufficient conditions for their boundedness or compactness. The results generalize the corresponding results on the single weighted composition operators and on the differences of composition operators, for example, M. Lindström and E. Wolf: Essential norm of the difference of weighted composition operators. Monatsh. Math. 153 (2008), 133--143