Let \(J\) be an interval with \(|I| = b\), \(p \in [1,\infty]\), \(\gamma \in (0,1]\), \(a\in \mathbb{R}_+^n\) and \(E \subset \mathbb{R}\) a \((\gamma, a)\)-thick set . Then two universal constants \(c_1, c_2>0\) exists such that
\[\lVert f \rVert_{L^p(\mathbb{R})} \le \Bigl(\frac{c_1}{\gamma}\Bigr)^{c_2(a \cdot b+1)}\lVert f\rVert_{L^p(E)}.\][1, Theorem 1]
Links Link to heading
Remarks Link to heading
- comparison to other results
- this result is qualitatively optimal.
See also Link to heading
References Link to heading
- O. Kovrijkine,
Some results related to the Logvinenko-Sereda theorem,
Proceedings of the American Mathematical Society, vol. 129, no. 10, p. 3037–3047, 2001. doi:10.1090/S0002-9939-01-05926-3