On Imbeddings between Weighted Orlicz Spaces

Abstract

Necessary and sufficient conditions are given for weight functions $\varrho$ and $\sigma$, which guarantee validity of the imbedding between the Orlicz spaces $L_{Q,\varrho }\hookrightarrow L_{P,\sigma }$. We make use of two methods: the first of them is a limit procedure leading to the imbedding of weighted Zygnwnd classes into weighted $L_1$, the second method employs the concept of duality in weighted Orlicz spaces, index of a Young function and results in a general imbedding theorem.