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Weighted fractional composition operators on certain function spaces. (English) Zbl 1508.47035

Summary: In this paper, we give some characterizations for the boundedness of weighted fractional composition operator \(D_{\varphi , u}^\beta\) from \(\alpha \)-Bloch spaces into weighted type spaces by deriving the bounds of its norm. Also, estimates for essential norm are obtained which gives necessary and sufficient conditions for the compactness of the operator \(D_{\varphi , u}^\beta \).

MSC:

47B33 Linear composition operators
33C05 Classical hypergeometric functions, \({}_2F_1\)
26A33 Fractional derivatives and integrals
44A35 Convolution as an integral transform
30H30 Bloch spaces
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