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On estimates of the approximation numbers of the Hardy operator

E. N. Lomakina<sup>ab

a</sup> Department of Higher Mathematics, Far Eastern State Transport University, 47 Seryshev St., Khabarovsk 680021, Russia
^b Department of Mathematics and Mathematical Methods in Economics, Khabarovsk State University of Economics and Law, 134 Tikhookeanskaya St., Khabarovsk 680042, Russia

Abstract: We obtain two–sided estimates which describe the behaviour of the approximation numbers of the Hardy operator and Schatten–Neumann norms in the new case, when the compact operator
$$ Tf(x)=\int_0^x f(\tau) d\tau, \quad x>0, $$
is acting from a Lebesgue space to a Lorentz space $(T: L_v^r(R^+)\to L_\omega^{pq}(R^+))$ under the condition $1<p<r\leqslant q<\infty$.

Keywords and phrases: Lebesgue space, Lorentz space, Hardy operator, approximation numbers, Schatten–von Neumann norm.

MSC: 47B06, 47G10, 47B10

Received: 14.04.2015

Language: English

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