On the angular distribution of mass by Besov functions

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 $f^{-1}(\Sigma_{\varepsilon})$.