Authors: Stević, Stevo 
Jiang, Zhi Jie
Title: Boundedness and essential norm of an integral-type operator on a Hilbert–Bergman-type spaces
Journal: Journal of Inequalities and Applications
Volume: 2019
Issue Date: 1-Jan-2019
Rank: M21
ISSN: 1029-242X
DOI: 10.1186/s13660-019-2077-8
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 Aγ,δ2(D) be the space of analytic functions that are L 2 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 I g on H(D) is defined as Igf(z)=∫0zf(ζ)g(ζ)dζ. In this paper, we characterize the boundedness of I g on Aγ,δ2, whereas in the main result we estimate the essential norm of the operator. Some basic results on the space Aγ,δ2(D) are also presented.
Keywords: Boundedness | Compactness | Essential norm | Integral-type operator
Publisher: Springer Link
Project: Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Sichuan Science and Technology Program (No. 2018JY0200)
Education Department of Sichuan Province (No. 18ZA0339)

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