Premium
An equivalence for weighted integrals of an analytic function and ist derivative
Author(s) -
Pavlović Miroslav,
Peláez José Ángel
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510701
Subject(s) - mathematics , equivalence (formal languages) , differentiable function , pure mathematics , derivative (finance) , analytic function , mathematical analysis , economics , financial economics
In this paper we introduce the class of differentiable weights ω in the unit disc such thatwhere L is a positive constant. The main result in this paper asserts that if ω is one of these weights, then the equivalenceholds for all 0 < p < ∞, 0 < q ≤ ∞and f an analytic function in . Our results improve others due to Aleman, Siskakis, and Stević. We also prove two results on harmonic conjugate functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)