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Multivariate Landau–Kolmogorov-type inequality

Published online by Cambridge University Press:  24 October 2008

Z. Ditzian
Z. Ditzian
Affiliation:
Department of Mathematics, Faculty of Science, University of Alberta, Edmonton, CanadaT6G 2G1
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Abstract

Assuming that the nth iterate of the Laplacian Δnf belongs to L∞(ℝ), we show for 0 < k < 2n that

where ∂/∂ξi is the derivative in the ei direction. The result is also extended to other Banach spaces of functions on ℝd.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 335 - 350
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

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