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

Ze-Hua Zhou;  Yu-Xia Liang — 2012

Czechoslovak Mathematical Journal

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 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....

Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball

Yu-Xia Liang;  Chang-Jin Wang;  Ze-Hua Zhou — 2015

Annales Polonici Mathematici

Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator u C φ on H() is defined by u C φ f ( z ) = u ( z ) f ( φ ( z ) ) . We investigate the boundedness and compactness of u C φ induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.

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