Volume 5, Issue 1 (Vol. 5, No. 1 2019)                   mmr 2019, 5(1): 1-8 | Back to browse issues page

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ardalani M. Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane. mmr 2019; 5 (1) :1-8
URL: http://mmr.khu.ac.ir/article-1-2659-en.html
, m.ardalani@uok.ac.ir
Abstract:   (2216 Views)
In this paper, we intend to show that without any certain growth condition on the weight function, we always able to present a weighted sup-norm on the upper half plane in terms of weighted sup-norm on the unit disc and supremum of holomorphic functions on the certain lines in the upper half plane.
Material and methods
We use a certain transform between the unit dick and the upper half-plane, a translation operator between weighted spaces of holomorphic functions toghther with Phragmen-Lindelof theorem in order to obtain our main results.
Results and discussion
We prove 3 Lemma which enable us to get our main results in Theorem 3.
The following conclusions were drawn from this research.
Full-Text [PDF 406 kb]   (431 Downloads)    
Type of Study: Original Manuscript | Subject: alg
Received: 2017/07/31 | Revised: 2019/07/9 | Accepted: 2018/04/3 | Published: 2019/07/13 | ePublished: 2019/07/13

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