دو نمايش معادل براي نرم فضاهاي وزن ‌دار از توابع تمام‌ ريخت روي نيم ‌صفحه بالايي

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

هدف مقاله اين است كه نشان دهيم بدون اين‌كه لازم باشد تابع وزن در شرايط رشدي خاصي صدق كند همواره نرم سوپريمم وزني روي نيم ‌صفحۀ بالايي را مي‌توان برحسب نرم سوپريمم وزني روي گوي يكه باز و هم‌چنين برحسب سوپريمم مقادير تابع تمام‌ريخت روي خط‌هاي خاصي در نيم‌ صفحۀ بالايي نمايش داد.

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.