Proceedings of the American Mathematical Society

Author(s): Adam Sikora; James Wright
Journal: Proc. Amer. Math. Soc. 129 (2001), 1745-1754.
MSC (2000): Primary 42B15; Secondary 35P99
Posted: October 31, 2000
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We show that if

is a second-order uniformly elliptic operator in divergence form on $\mathbf{R}^d$ , then $C_1(1+\vert\alpha\vert)^{d/2} \le \Vert L^{i\alpha}\Vert _{L^1 \to L^{1,\infty}} \le C_2 (1+\vert\alpha\vert)^{d/2}$ . We also prove that the upper bounds remain true for any operator with the finite speed propagation property.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B15, 35P99

Adam Sikora
Affiliation: Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia (or University of Wroclaw, KBN 2 P03A 058 14, Poland)
Email: sikora@maths.anu.edu.au

James Wright
Affiliation: School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia
Address at time of publication: Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3JZ, United Kingdom
Email: jimw@maths.unsw.edu.au, wright@maths.ed.ac.uk

DOI: 10.1090/S0002-9939-00-05754-3
PII: S 0002-9939(00)05754-3
Keywords: Spectral multiplier, imaginary powers
Received by editor(s): June 22, 1999
Received by editor(s) in revised form: September 27, 1999
Posted: October 31, 2000
Additional Notes: The research for this paper was supported by the Australian National University, the University of New South Wales, the University of Wroclaw, the Australian Research Council and the Polish Research Council KBN. We thank these institutions for their contributions.
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 2000, American Mathematical Society

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