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On a Peetre functional
G. M. Berkolaiko Voronezh State University
Abstract:
The Peetre $K$-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 Peetre $K_2$-functional
$$
K_2(t,\mathbf x)=\inf_{\mathbf x=\mathbf x_1+\mathbf x_2}\sqrt{\|\mathbf x_1\|_1^2+t^2\|\mathbf x_2\|_2^2}
$$
is treated as a function of $t$ for fixed $\mathbf x$, and its properties are studied. Several particular cases are considered and classes of functions expressible as $K_2(t)$ are investigated.
Received: 23.09.1994
Citation:
G. M. Berkolaiko, “On a Peetre functional”, Mat. Zametki, 61:1 (1997), 26–33; Math. Notes, 61:1 (1997), 22–28
Linking options:
https://www.mathnet.ru/eng/mzm1479https://doi.org/10.4213/mzm1479 https://www.mathnet.ru/eng/mzm/v61/i1/p26
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