The space of multipliers and convolutors of Orlicz spaces on a locally compact group
Volume 219 / 2013
Abstract
Let be a locally compact group, let (\varphi , \psi ) be a complementary pair of Young functions, and let L^\varphi (G) and L^\psi (G) be the corresponding Orlicz spaces. Under some conditions on \varphi , we will show that for a Banach L^\varphi (G)-submodule X of L^\psi (G), the multiplier space \mathop {\rm Hom}_{L^\varphi (G)}(L^\varphi (G),X^*) is a dual Banach space with predual L^\varphi (G)\bullet X :=\overline {{\rm span}}\{ ux: u\in L^\varphi (G), x\in X \}, where the closure is taken in the dual space of \mathop {\rm Hom}_{L^\varphi (G)}(L^\varphi (G),X^*). We also prove that if \varphi is a \Delta _2-regular N-function, then \mathop {\rm Cv}_{{\varphi }}(G), the space of convolutors of M^\varphi (G), is identified with the dual of a Banach algebra of functions on G under pointwise multiplication.
