Abstract. We consider the commutator operator $[B, \sigma(x,D)]$ of the multiplication operator by a function $B$ and a pseudo-differential operator $\sigma(x,D)$, and prove that $[B, \sigma(x,D)]$ is bounded on the local Hardy spaces $h^p({\msbm R}^n)$. We also show that our result is optimal.
AMS Subject Classification
(1991): 42B20
Keyword(s):
pseudo-differential operator,
commutator,
Hardy space,
local Hardy space
Received January 13, 2009, and in revised form April 11, 2011. (Registered under 7/2009.)
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