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Asymmetric approximations in the spaceL p(t)

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Abstract

We introduce the notion of (α,β)-norm in the spaceL p(t) of functionsx(t) for which

$$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< \infty } $$

wherep(t) is a positive measurable function. We establish a criterion for the element of the best (α,β)-approximation in the spaceL p(t). We obtain inequalities of the type of duality relations.

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Authors
  1. O. V. Polyakov
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  2. E. G. Litvin
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Additional information

Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7., pp. 952–959, July, 1999.

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Polyakov, O.V., Litvin, E.G. Asymmetric approximations in the spaceL p(t) . Ukr Math J 51, 1069–1078 (1999). https://doi.org/10.1007/BF02592042

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  • DOI: https://doi.org/10.1007/BF02592042

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