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Norms and Essential Norms of Differences of Weighted Composition Operators

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Abstract

We obtain the norm and essential norm estimates for the difference of two weighted composition operators from a weighted Bergman space \(A^p_{\alpha }\) into a Lebesgue space \(L^q(\mu )\), where \(0 < p \le q\), \(\alpha > -1\) and \(\mu \) is a positive Borel measure on the unit disk of \({{\mathbb {C}}}\). The weights of the weighted maps in this paper are not necessarily analytic or bounded. Consequently, characterizations for the boundedness and compactness of the difference operator are established.

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  1. Division of Science, Engineering and Health Studies College of Professional and Continuing Education, The Hong Kong Polytechnic University, Hong Kong, China

    Ching-on Lo

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  1. Ching-on Lo
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Lo, Co. Norms and Essential Norms of Differences of Weighted Composition Operators. Mediterr. J. Math. 19, 210 (2022). https://doi.org/10.1007/s00009-022-02146-8

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  • DOI: https://doi.org/10.1007/s00009-022-02146-8

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