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STUDIA MATHEMATICA - Issue no. 1 / 2007 | |||||||
Article: |
ON THE APPROXIMATION NUMBERS OF CERTAIN VOLTERRA INTEGRAL OPERATORS BETWEEN LEBESGUE SPACES. Authors: MOHAMED ACHACHE. |
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Abstract:
The aim of the paper is to study certain Volterra integral operators of the form which defines linear maps between the Lebesgue spaces Lp(R ) and Lq(R ) where 1 < q < p < oo. Under some conditions of the integrability on its kernel, we show some important properties for T such as boundedness, compactness, the measureof non compactness and estimating, upper and lower bounds for its approximation numbers. These estimates have an application to the spectral properties of Sturm-Liouville differential operators. |
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