Two new classes of subalgebras of \(L^1(G)\) (Q2341411)

If \(L^{p,q;b}(G)\) are the Lorentz-Karamata spaces on a locally compact abelian group \(G\) (where \(b\) is a slowly varying function, in the sense of Karamata, on \([1,\infty)\)), then properties of the algebras \(A_{p,q;b}(G):= \{f\in L^1(G): \widehat{f}\in L^{p,q;b}(\widehat{G})\}\) and \(B_{p,q;b}(G):=L^1(G)\cap L^{p,q;b}(G)\), completely analogous to the known ones for \(A_p(G):= \{f\in L^1(G): \widehat{f}\in L^p(\widehat{G})\}\) and \(L^1\cap L^p(G)\) (and similarly spaces when \(L^p\) is replaced by \(L^{p,q}\)) are listed. The multiplier algebra of \(B_{p,q;b}(G)\) is identified.