Bulletin of the Belgian Mathematical Society - Simon Stevin

On the angular distribution of mass by Besov functions

René Erlín Castillo and Julio C. Ramos Fernández

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Abstract

Let $\Bbb D$ be the open unit disk in the complex plane. For $\varepsilon \gt 0$ we consider the sector $\Sigma_{\varepsilon} = \{z\; : \; |\arg z | \lt \varepsilon \}$. We will prove that for certain classes of functions $f$ in the Besov's space $B_p\left(\Bbb D\right)$ such that $f(0)=0$, the $B_p$ norm is obtained by integration over $f^{-1}(\Sigma_{\varepsilon})$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 2 (2007), 303-310.

Dates
First available in Project Euclid: 22 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1179839221

Digital Object Identifier
doi:10.36045/bbms/1179839221

Mathematical Reviews number (MathSciNet)
MR2341564

Zentralblatt MATH identifier
1129.30001

Subjects
Primary: 30C25: Covering theorems in conformal mapping theory
Secondary: 30H05: Bounded analytic functions 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
Besov's spaces conformal mappings

Citation

Erlín Castillo, René; Ramos Fernández, Julio C. On the angular distribution of mass by Besov functions. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 2, 303--310. doi:10.36045/bbms/1179839221. https://projecteuclid.org/euclid.bbms/1179839221


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