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Local square summability of convolutions

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Abstract

Let ℘(D) and R(D) be two convolution operators in ℓn and K be an arbitrary compact subset of ℝn, having interior points. Necessary and sufficient conditions are given for the boundedness and compactness of the ball

in the metric of\(\left\| {\mathcal{R}\left( D \right)u} \right\|_{L^ \propto \left( K \right)} \).

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Literature cited

  1. L. Hörmander, Linear Partial Differential Operators [Russian translation], Mir, Moscow (1965).

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Authors
  1. V. G. Maz'ya
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 211–216, 1977.

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Maz'ya, V.G. Local square summability of convolutions. J Math Sci 34, 2148–2152 (1986). https://doi.org/10.1007/BF01741591

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  • DOI: https://doi.org/10.1007/BF01741591

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