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On theL p-L q-estimates for the solutions of certain hyperbolic equations

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Abstract

We establish conditions, which should be imposed on the exponentsp andq and the dimensionalityn of a space in order that theL p-L q-estimates should hold for the solutions of the Cauchy problem for a second-order hyperbolic equation with constant coefficients.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    A. I. Markovskii

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  1. A. I. Markovskii
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 992–1008, July, 1993.

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Markovskii, A.I. On theL p-L q-estimates for the solutions of certain hyperbolic equations. Ukr Math J 45, 1101–1120 (1993). https://doi.org/10.1007/BF01057457

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  • DOI: https://doi.org/10.1007/BF01057457

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