On an integral-type operator from the Bloch space to mixed norm spaces
Applied Mathematics and Computation(2016)
Abstract
Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0)=0, where H(B) is the space of all holomorphic functions on the unit ball B of Cn. In this paper we investigate the following integral-type operator
Dφgf(z)=∫01Df(φ(tz))g(tz)dtt,f∈H(B),where Df is the fractional derivative of f ∈ H(B). The boundedness and compactness of the operators Dφg between mixed norm spaces and Bloch spaces in the unit ball are studied.
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Key words
Integral-type operator,Mixed norm space,Bloch space,Boundedness,Compactness
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