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ON THE APPROXIMATION NUMBERS OF CERTAIN VOLTERRA INTEGRAL OPERATORS BETWEEN LEBESGUE SPACES

The aim of the paper is to study certain Volterra integral op- erators of the form Tf(x) = v(x) R x 0 u(t)f(t)dt which defines linear maps between the Lebesgue spaces L p (R + ) and L q (R + ) where 1 q < p +1. Under some conditions of the integrability on its kernel, we show some im- portant properties for T such as boundedness, compactness, the measure of non compactness and estimating, upper and lower bounds for its ap- proximation numbers. These estimates have an application to the spectral properties of Sturm-Liouville dierential operators.