Ultraproducts of real interpolation spaces between L
p
-spaces |
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Authors: | J A López Molina M E Puerta M J Rivera |
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Institution: | (1) E.T.S. Ingenieros Agrónomos, Universidad Politécnica de Valencia, Camino de Vera, 46072 Valencia, SPAIN;(2) Universidad Eafit, Carrera 49 7Sur-50, 3300 Medellín, COLOMBIA |
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Abstract: | Let
, be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter
in
, the ultraproduct
of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type
, an intermediate K?the space between
and
being a purely atomic measure space, and a K?the function space K(Ω3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅.
The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group
03/050. |
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Keywords: | ultraproducts interpolation spaces |
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