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On a Peetre functional

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Abstract

The PeetreK-functional is often used to describe and study the interpolation spaces associated with the real variable method. In the paper a modification of this functional, the PeetreK 2-functional

$$K_2 (t,x) = \mathop {\inf }\limits_{x = x_1 + x_2 } \sqrt {\left\| {x_1 } \right\|_1^2 + t^2 \left\| {x_2 } \right\|_2^2 } ,$$

is treated as a function oft for fixed x, and its properties are studied. Several particular cases are considered and classes of functions expressible asK 2(t) are investigated.

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References

  1. J. Bergh and J. Löfstrom,Interpolation Spaces. An Introduction, Springer-Verlag, Heidelberg (1976).

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Authors and Affiliations

  1. Voronezh State University, Voronezh, USSR

    G. M. Berkolaiko

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  1. G. M. Berkolaiko
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Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 26–33, January, 1997.

Translated by N. K. Kulman

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Berkolaiko, G.M. On a Peetre functional. Math Notes 61, 22–28 (1997). https://doi.org/10.1007/BF02355004

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  • DOI: https://doi.org/10.1007/BF02355004

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