Abstract
In the last chapter, we developed an operator calculus and used it for several purposes, including obtaining commutator estimates in §3.6. Here we work in the opposite order. In §4.1 we recall the estimate (3.6.2) of Coifman-Meyer (generalizing results of Calderon) and show how it leads to further commutator estimates for operators with C1-regular symbols. Then we use these commutator estimates to establish an operator calculus for symbols in C1S mcl . For this, Calderon’s estimates suffice, and much of the material of §4.2 is contained in [Ca2], [Ca3]. In §4.3, we look at a Gårding inequality, more precise, though less general, than the Gårding inequality in Proposition 2.4.B.
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© 1991 Springer Science+Business Media New York
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Taylor, M.E. (1991). Calculus for OPC1S mcl . In: Pseudodifferential Operators and Nonlinear PDE. Progress in Mathematics, vol 100. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0431-2_6
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DOI: https://doi.org/10.1007/978-1-4612-0431-2_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3595-4
Online ISBN: 978-1-4612-0431-2
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