Optimal extension of the Fourier transform and convolution operator on compact groups

Abstract

Let $G$ be a compact group (not necessarily abelian) and let $\hat{I}¦$ be a Young function satisfying the $\hat{I}{”}_2$-condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces $L^{\hat{I}}¦(G).$