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Integrating Over the Inverse Image of Functions in the Besov Space

  • Julio C. Ramos-Fernández
Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 15 Issue 1

Abstract

Let 𝔻 be the open unit disk in the complex plane. For ε > 0 we consider the sector ∑ε = {𝑧 : |arg 𝑧| < ε}. We prove that for certain classes of functions 𝑓 in the Besov space (𝔻) such that 𝑓(0) = 0, the norm is obtained by integration over 𝑓–1(∑ε).

Key words and phrases:: Besov space; conformal mapping
Received: 2006-11-16
Published Online: 2010-03-10
Published in Print: 2008-March

© Heldermann Verlag

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