Spaces Λα(X) and interpolation |
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Authors: | Robert Sharpley |
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Institution: | Department of Mathematics, Oakland University, Rochester, Michigan 48063 U.S.A. |
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Abstract: | For two pairs of rearrangement invariant spaces α = (X1, Y1), (X2, Y2)] we give necessary and sufficient conditions for pairs (X, Y) to be weak intermediate for σ, i.e., each operator which is of weak types (Xi, Yi), i = 1, 2, also maps X boundedly to Y. Spaces Λα(X) are introduced and are shown to have many of the properties that characterize Lorentz Lpq spaces. Necessary and sufficient conditions in terms of a simple function F(s, t) are given in order that (Λα(X), Λα(Y)) be weak intermediate for σ. Other properties of the function F(s, t) yield sufficient conditions and necessary conditions for interpolation theorems. |
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