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Reiteration formulae for interpolation methods associated to polygons

Cobos, Fernando and Richter, Christian and Ullrich, Tino (2009) Reiteration formulae for interpolation methods associated to polygons. Journal of Mathematical Analysis and Applications, 352 (2). pp. 773-787. ISSN 0022-247X

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Abstract

We study spaces generated by applying the interpolation methods defined by a polygon Π
to an N-tuple of real interpolation spaces with respect to a fixed Banach couple {X, Y }. We
show that if the interior point (α,β) of the polygon does not lie in any diagonal of Π then
the interpolation spaces coincide with sums and intersections of real interpolation spaces
generated by {X, Y }. Applications are given to N-tuples formed by Lorentz function spaces
and Besov spaces. Moreover, we show that results fail in general if (α,β) is in a diagonal.


Item Type:Article
Uncontrolled Keywords:Banach-Spaces; Compact-Operators; Duality; Interpolation methods associated to polygons; Reiteration; Lorentz function spaces; Besov spaces; Mathematics, Applied; Mathematics
Subjects:Sciences > Mathematics > Topology
ID Code:14927
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