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Volterra-type operators from analytic Morrey spaces to Bloch space. (English) Zbl 1329.47035

This paper characterizes the continuity and compactness of the integral operators of Volterra type \(I_g(f)(z)=\int_0^z f'(z)g(z)\, dz\) and \(T_g(f)(z)=\int_0^z f(z)g'(z)\, dz\), for an analytic function \(g\) on the unit disc of the complex plane, when they act from an analytic Morrey space \(\mathcal{L}^{2,\lambda}\) into the Bloch space \(\mathcal{B}\), in terms of the symbol \(g\). The norm and the essential norm of these operators is also investigated. In the last section, the authors also consider these operators between the little spaces \(\mathcal{L}_0^{2,\lambda}\) and \(\mathcal{B}_0\).

MSC:

47B38 Linear operators on function spaces (general)
30H30 Bloch spaces
30H99 Spaces and algebras of analytic functions of one complex variable
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