دو نمایش معادل برای نرم فضاهای وزن‌دار از توابع تمام‌ریخت روی نیم‌صفحه بالایی

نویسنده
محمد علی اردلانی
دانشگاه کردستان، دانشکدۀ علوم پایه، گروه ریاضی
10.29252/mmr.5.1.1
چکیده
هدف مقاله این است که نشان دهیم بدون این‌که لازم باشد تابع وزن در شرایط رشدی خاصی صدق کند همواره نرم سوپریمم وزنی روی نیم‌صفحۀ بالایی را می‌توان برحسب نرم سوپریمم وزنی روی گوی یکه باز و هم‌چنین برحسب سوپریمم مقادیر تابع تمام‌ریخت روی خط‌های خاصی در نیم‌صفحۀ بالایی نمایش داد.
کلیدواژه‌ها
تابع تمام‌ریخت
وزن استاندارد
فضاهای وزن‌دار
نیم‌صفحه بالایی

عنوان مقاله English

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

نویسنده English

ma ardalani
چکیده English

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./files/site1/files/51/%D8%A7%D8%B1%D8%AF%D9%84%D8%A7%D9%86%DB%8C.pdf

کلیدواژه‌ها English

Holomorphic function
Standard weight
Weighted spaces
Upper half plane
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