Abstract
For interpolation in the diagonal case, i.e. with respect to the two couples (X, X) and (Y, Y), there exists a natural relation between weak-type and strong-type interpolation. Indeed, weak-type interpolation is related to the “M-couples” (ΛX, MX) and (ΛY, MY) of the Lorentz spaces of X and Y. Since ΛZ ⊂ MZ for any space Z, any weak-type interpolation space also has the (strong-type) interpolation property for the “Λ-couples” (ΛX, ΛX) and (ΛY, ΛY). In this paper a scale \({cal G}, c>0\), of interpolation functors with respect to the Λ-couples is introduced such that all generated interpolation spaces (also) have the weak-type interpolation property. Moreover, we will show that a space is a weak interpolation space if and only if it is generated by one of these functors.
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This paper covers a part of the material presented by the second named author in lectures at the DMV-Jahrestagung at Ulm, Germany, on September 18, 1995, as well at Voronezh State University, Russia, on September 13, 1996, during his six-week stay there.
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Fehér, F., Strauss, M.J. Interpolation Functors In Weak-Type Interpolation. Results. Math. 31, 95–104 (1997). https://doi.org/10.1007/BF03322152
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DOI: https://doi.org/10.1007/BF03322152