Boundedness and essential norm of an integral-type operator on a Hilbert-Bergman-type spaces

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Title:	Boundedness and essential norm of an integral-type operator on a Hilbert-Bergman-type spaces
Authors:	Stevo Stević
Contributors:	資訊工程學系
Date:	2019-03
Issue Date:	2019-11-08 02:38:43 (UTC+0)
Abstract:	Let D be the open unit disk of the complex plane C and H(D) be the space of all analytic functions on D. Let A2γ,δ(D) be the space of analytic functions that are L2 with respect to the weight ωγ,δ(z)=(ln1\|z\|)γ[ln(1−1ln\|z\|)]δ, where −1<γ<∞ and δ≤0. For given g∈H(D), the integral-type operator Ig on H(D) is defined as Igf(z)=∫z0f(ζ)g(ζ)dζ. In this paper, we characterize the boundedness of Ig on A2γ,δ, whereas in the main result we estimate the essential norm of the operator. Some basic results on the space A2γ,δ(D) are also presented.
Relation:	JOURNAL OF INEQUALITIES AND APPLICATIONS
Appears in Collections:	[Department of Computer Science and Information Engineering] Journal Artical

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