Fourier decompositions with positive coefficients in compact Gelfand pairs

For $G$ a compact separable Hausdorff topological group and for $1 < p \leqslant 2$ the finiteness of the Hausdorff-Young sequence operator is established for functions in ${L^1}(G)$ with positive Fourier decompositions and which are $p$th-power integrable in a neighborhood of the identity. A similar result is established in the context of compact Gelfand pairs.