Structure Constants of the Weyl Calculus

Wen Deng

Abstract


We find some explicit bounds on the $\mathcal{L}(L^2)$-norm of pseudo-differential operators with symbols defined by a metric on the phase space. In particular, we prove that this norm depends only on the "structure constants" of the metric and a fixed semi-norm of the symbol. Analogous statements are made for the Fefferman-Phong inequality.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15236

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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