\[ \DeclareMathOperator{\supp}{supp} \]

Let \(I\) be an interval with \(|I| = b\), \(p \in [1,\infty]\), \(\gamma \in (0,1]\), \(a>0\) and \(S \subset \mathbb{R}\) a \((\gamma, a)\)-thick set . Then a numerical constant \(C>0\) exists sucht that

\begin{equation*} \lVert f \rVert_{L^p(\mathbb{R})} \le \exp\Bigl(-C\frac{ab+1}{\gamma}\Bigr)\lVert f\rVert_{L^p(S)}, \end{equation*}

for every \(f\in L^p(\mathbb{R})\) with \(\supp \hat{f} \subset Q\) [1, p. 113].

See also Link to heading

• Kovrijkine’s improved version .
• Dicke’s and Veselić’s version on the sphere

References Link to heading

1. V. Havin and B. Jöricke, The Uncertainty Principle in Harmonic Analysis. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. doi:10.1007/978-3-642-78377-7