The $L^{p}$-conjecture and Young's inequality
The $L^{p}$-conjecture and Young's inequality
Let G be an arbitrary locally compact (Hausdorff) group.The conjecture in the title asserts that if L P(G) is closed under convolution for some p (1, o), then G is compact.In the present paper, we shall confirm this conjecture.In his 1961 paper [17], W. Zelazko solved the problem for all …