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Information Journal Paper

Title

Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane

Pages

  1-8

Abstract

 Introduction: 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. Conclusion: The following conclusions were drawn from this research. We find lower bound and upper bound for weighted sup-norm in terms of supremum of the function on the lines in the upper half-plane. We obtain lower and upper bounds for translation operator in terms of weighted Sup-norm.

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    • Cite

    APA: Copy

    Ardalani, M.a.. (2019). Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane. MATHEMATICAL RESEARCHES, 5(1 ), 1-8. SID. https://sid.ir/paper/260766/en

    Vancouver: Copy

    Ardalani M.a.. Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane. MATHEMATICAL RESEARCHES[Internet]. 2019;5(1 ):1-8. Available from: https://sid.ir/paper/260766/en

    IEEE: Copy

    M.a. Ardalani, “Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane,” MATHEMATICAL RESEARCHES, vol. 5, no. 1 , pp. 1–8, 2019, [Online]. Available: https://sid.ir/paper/260766/en

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