On maximizers of convolution operators in $L_{p}(\mathbb{R}^{n})$

Abstract

We discuss some facts and open problems related to maximizers of convolution operators with kernels in $L_{q}(\mathbb{R}^{n})$ from the perspective of our existence theorem (Sbornik Mathematics, 2019). The results on evaluation of $L_{p}\rightarrow L_{p^{\prime}}$ norms of the Laplace transform, which motivated this research, are reported.