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Adjoint of generalized Cesáro operators on analytic function spaces. (English) Zbl 1462.30109

Summary: In this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by K. Avetisyan and S. Stević in [Appl. Math. Comput. 213, No. 2, 304–311 (2009; Zbl 1167.30325)]. Also we consider the adjoint \(\mathcal{A}^{b,c}\) for \(b> 0\) of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces \(B_{\alpha+(c-1)}^{p,q}\) for \(c> 1\).

MSC:

30H25 Besov spaces and \(Q_p\)-spaces
30H30 Bloch spaces
47B33 Linear composition operators

Citations:

Zbl 1167.30325
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Full Text: DOI

References:

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