The preprint On the existence of optimizers for nonlinear time-frequency concentration problems: the Wigner distribution, a joint work with Federico Stra and Erling Svela, is now available on arXiv (arXiv:2510.18683).
We prove that, for any measurable phase space subset \(\Omega\subset\mathbb{R}^{2d}\) with \(0<|\Omega|<\infty\) and any \(1\le p < \infty\), the nonlinear concentration problem
\(\displaystyle \sup_{f \in L^2(\mathbb{R}^d)\setminus\{0\}}\frac{\|Wf\|_{L^p(\Omega)}}{\|f\|_{L^2}^2} \)
has an optimizer, where \(Wf\) is the Wigner distribution of \(f\).
We also discuss some related problems for \(\tau\)-Wigner and Born-Jordan distributions.