We will look at the following problem on timefrequency localization: What is the norm of the point evaluation functional in the classical PaleyWiener $L^p$ spaces for $0 < p <\infty$? The central challenge in this problem is how to go beyond the power trick which allows you to relate an estimate for a given $p$ to that for $kp$ for a positive integer $k$. I will discuss some results and multiple conjectures around this problem. The talk is based on recent joint work with Ole Fredrik Brevig, Andrés Chirre, and Joaquim Ortega-Cerdà (see https://arxiv.org/abs/2210.13922).