Imaginary powers of laplace operators

Adam Sikora; James Wright

doi:10.1090/s0002-9939-00-05754-3

Imaginary powers of laplace operators

Adam Sikora^*, James Wright

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

Abstract

We show that if L is a second-order uniformly elliptic operator in divergence form on R^d, then C₁(1+|a|)^d/2 < \\L^ia\\Li→L1,∞ ≥ C₂(1+|a|)^d/2. We also prove that the upper bounds remain true for any operator with the finite speed propagation property.

Original language	English
Pages (from-to)	1745-1754
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	129
Issue number	6
DOIs	https://doi.org/10.1090/s0002-9939-00-05754-3
Publication status	Published - 2001

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abstract = "We show that if L is a second-order uniformly elliptic operator in divergence form on Rd, then C1(1+|a|)d/2 < \\Lia\\Li→L1,∞ ≥ C2(1+|a|)d/2. We also prove that the upper bounds remain true for any operator with the finite speed propagation property.",

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AB - We show that if L is a second-order uniformly elliptic operator in divergence form on Rd, then C1(1+|a|)d/2 < \\Lia\\Li→L1,∞ ≥ C2(1+|a|)d/2. We also prove that the upper bounds remain true for any operator with the finite speed propagation property.

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JO - Proceedings of the American Mathematical Society

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Imaginary powers of laplace operators

Abstract

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