Some intersections of the weighted \(L^p\)-spaces (Q2319345)

Summary: Let \(G\) be a locally compact group \(\Omega\) an arbitrary family of the weight functions on \(G\), and \(1 \leq p < \infty\). The locally convex space \(I L_p(G, \Omega)\) as a subspace of \(\cap_{\omega \in \Omega} L^p(G, \omega)\) is defined. Also, some sufficient conditions for that space to be a Banach space are provided. Furthermore, for an arbitrary subset \(J\) of \([1, \infty)\) and a positive submultiplicative weight function \(\omega\) on \(G\), Banach subspace \(I L_J(G, \omega)\) of \(\cap_{p \in J} L^p(G, \omega)\) is introduced. Then some algebraic properties of \(I L_J(G, \omega)\), as a Banach algebra under convolution product, are investigated.