ON SOME EMBEDDING THEOREMS FOR IDEAL STRUCTURES

For general ideal structures involving symmetric spaces, the following embedding is proved: E subset of L-1 + L-infinity. For a class of ideal structures involving symmetric spaces, it is proved that L-1 boolean AND L-infinity subset of E subset of L-1 + L-infinity. Embedding theorems for symmetric spaces with bounded measurable support are proved in terms of the norms of the extension operators and in terms of Boyd indices (see [20]). A new space (M-phi) over bar called the generalized Marcinkiewicz space is introduced. The following embedding is proved: E subset of <(M-phi E(1))over bar>, where phi(E) (t) = parallel to chi([0, t])(s)parallel to(E).