Abstract duality Sawyer formula and its applications


The main subject of this paper is to present some general results on duality and Banach envelopes of a large class of symmetric quasi-Banach spaces. An abstract duality formula, a general form of the Sawyer's characterization of the reverse Hölder inequality for L p -spaces, 1 < p < ∞, in function ideals is proved. This formula is then applied for characterization of Köthe duals of rearrangement invariant (r.i.) function lattices. A duality formula for 1-concave quasi-Banach function lattices is shown and it is employed to characterize Banach envelopes of r.i. quasi-Banach lattices. As applications of the duality formulas to quasi-normed Orlicz-Lorentz spaces, a description of their Köthe duals and of their Banach envelopes is presented. The conditions for normability as well as for boundedness of Hardy-Littlewood maximal operator are also given in some class of Orlicz-Lorentz spaces. © Springer-Verlag 2007.

Publication Title

Monatshefte fur Mathematik