RMC - Vol. 2, supplementary - A. Kaminska/J. Musielak

Full paper in PDF:
$% A. Kamińska and J. Musielak, On convolution operator in Orlicz spaces, Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 157–178.%$

On Convolution Operator in Orlicz Spaces

Anna KAMIŃSKA and Julian MUSIELAK

Institute of Mathematics
A. Wiszniewski
Poznan — Poland

ABSTRACT

The Orlicz spaces defined on a locally compact Abelian group are considered. The main results consist in presenting sufficient and necessary conditions, expressed in terms of generated functions $fi$ , for embeddings $Lf1 *Lf2 --> Lf3$ , $Ef1 *Ef2 --> Ef3$ , $Ef1 *Ef2 --> Lf3$ , and $Lf1 *Lf2 --> Ef3$ , where $Lfi$ are Orlicz spaces and $Efi$ are their subspaces consisting of all order continuous elements. Some results of the paper are an extension and generalization of those contained in Hewitt and Ross (1979), Hudzik et al. (1985), O’Neil (1965), and Zelazko (1961).

1980 Mathematics Subject Classification (1985 revision): 46E30.