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ON THE BOUNDEDNESS AND COMPACTNESS OF A CLASS OF INTEGRAL OPERATORS

Published online by Cambridge University Press:  01 April 2000

DMITRII V. PROKHOROV
DMITRII V. PROKHOROV
Affiliation:
Computer Center of the Far Eastern Branch of the Russian Academy of Sciences, Tikhookeanskaya 153, Khabarovsk 680042, Russia; prohorov@as.dv.khv.ru
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Abstract

Let α > 0. The operator of the form

formula here

is considered, where the real weight function v(x) is locally integrable on R+ := (0, ∞). In case v(x) = 1 the operator coincides with the Riemann–Liouville fractional integral, Lp → Lq estimates of which with power weights are well known. This work gives Lp → Lq boundedness and compactness criteria for the operator Tα in the case 0 < p, q < ∞, p > max(1/α, 1).

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 617 - 628
Copyright
The London Mathematical Society 2000

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