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An equivalence for weighted integrals of an analytic function and ist derivative

✍ Scribed by Miroslav Pavlović; José Ángel Peláez

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 146 KB
Volume: 281
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200510701

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper we introduce the class of differentiable weights ω in the unit disc 𝔻 such that

equation image

where L is a positive constant.

The main result in this paper asserts that if ω is one of these weights, then the equivalence

equation image

holds for all 0 < p < ∞, 0 < q ≤ ∞and f an analytic function in 𝔻. Our results improve others due to Aleman, Siskakis, and Stević.

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