ON THE BOUNDEDNESS AND COMPACTNESS OF A CLASS OF INTEGRAL OPERATORS

DMITRII V. PROKHOROV

doi:10.1112/S002461079900856X

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).

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ON THE BOUNDEDNESS AND COMPACTNESS OF A CLASS OF INTEGRAL OPERATORS

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ON THE BOUNDEDNESS AND COMPACTNESS OF A CLASS OF INTEGRAL OPERATORS

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