An Optimization Problem and Point-Evaluation in Paley–Wiener Spaces

We study the constant Cₚ C p defined as the smallest constant C such that |f(0)|ᵖ ≤ C f ₚᵖ | f ( 0 ) | p ≤ C ‖ f ‖ p p holds for every function f in the Paley–Wiener space PWᵖ PW p . Brevig, Chirre, Ortega-Cerdà, and Seip have recently shown that Cₚ C p < p / 2 for allp>2$$ p > 2 . We improve this bound for $$2 2 < p ≤ 5 by solving an optimization problem.