Commutator estimates for Hölder continuous and bmo-Sobolev multipliers

Taylor, Michael

doi:10.1090/proc/12825

Commutator estimates for Hölder continuous and bmo-Sobolev multipliers
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by Michael E. Taylor PDF

Proc. Amer. Math. Soc. 143 (2015), 5265-5274 Request permission

Abstract:

We discuss conditions on a function $f$ under which the commutator $[P,f]$ of a pseudodifferential operator $P$ of order $m$ with the operation of multiplication by $f$ is an operator of order $m-r$ on various function spaces, namely Hölder-Zygmund spaces and $L^p$-Sobolev spaces, given $0<r<1$. We also establish an endpoint case involving $r=1$, and we extend the scope to all $r>0$ for a particularly significant case in 1 dimension.

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