Imaginary powers of Laplace operators

Research Report MRR99-037

Imaginary powers of Laplace operators

Adam Sikora, James Wright

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

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