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Estimates of essential norms of weighted composition operators between Bloch-type spaces. (English) Zbl 1267.47040

The authors of the present paper obtain estimates of the essential norm of weighted composition operators acting on Bloch type spaces in terms of the powers of the symbol. Previously, R.-H. Zhao [Proc. Am. Math. Soc. 138, No. 7, 2537–2546 (2010; Zbl 1190.47028)] gave a formula for the essential norm of a composition operator on Bloch space in terms of the powers of the symbol. More recently, J. S. Manhas and R.-H. Zhao [J. Math. Anal. Appl. 389, No. 1, 32–47 (2012; Zbl 1267.47042)] gave estimates on Bloch type spaces, except for the Bloch space itself. The authors of the present paper also obtain estimates for the Bloch space. The first work in which the essential norm of a composition operator acting on Bloch space was exactly given is [A. Montes-Rodríguez, Pac. J. Math. 188, No. 2, 339–351 (1999; Zbl 0932.30034)].

MSC:

47B33 Linear composition operators
46E15 Banach spaces of continuous, differentiable or analytic functions
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References:

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