Sharp estimates for pseudodifferential operators with symbols of limited smoothness and commutators

David Lannes

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Sharp estimates for pseudodifferential operators with symbols of limited smoothness and commutators

David Lannes

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Abstract

We consider here pseudo-differential operators whose symbol $σ(x,ξ)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive sharp estimates on the action of such pseudo-differential operators on Sobolev spaces and give explicit expressions for their operator norm in terms of the symbol $σ(x,ξ)$. We also study commutator estimates involving such operators, and generalize or improve the so-called Kato-Ponce and Calderon-Coifman-Meyer estimates in various ways.

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David Lannes. 2005-08-24. Sharp estimates for pseudodifferential operators with symbols of limited smoothness and commutators. https://arxiv.org/abs/math/0508465

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