On maximizers of convolution operators in $L_p$ spaces

Gleb Kalachev, Sergey Sadov

A convolution operator in ${\mathbb{R}}^d$ with kernel in $L_q$ acts from $L_p$ to $L_s$, where $1/p+1/q=1+1/s$. The main theorem states that if $1<q,p,s<\infty$, then there exists a…