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Certain reiteration and equivalence results for the Cobos-Peetre polygon interpolation method
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
1999 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 85, no 2, 310-319 p.Article in journal (Refereed) Published
Abstract [en]

We prove some reiteration formulas for the Cobos-Peetre polygon method for $n+1$ tuples that consists of spaces $A_i$ where $A_i$ is of class $\theta_i$ with respect to a compatible pair $(X,Y)$. If $\theta_i$ is suitably chosen, the $J$- and $K$-method coincides and is equal to a space $(X,Y)_{\nu,q}$. For arbitrary chosen $\theta_i$ the $J$- and $K$-spaces will not, in general, coincide. In particular, we show that interpolation of Lorentz spaces over the unit square yields that the $K$-space is the sum of two Lorentz spaces whereas the $J$-space is the intersection of the same two Lorentz spaces.

Place, publisher, year, edition, pages
1999. Vol. 85, no 2, 310-319 p.
Research subject
URN: urn:nbn:se:ltu:diva-13447Local ID: caae3180-88b3-11dd-9d47-000ea68e967bOAI: diva2:986400
Godkänd; 1999; 20080922 (ysko)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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