Let L=-div(A∇) be a second order divergence form elliptic operator, where A is an accretive, n×n matrix with bounded measurable complex coefficients on Rn. Let Lα/2 (0 < α < 1) denotes the fractional differential operator associated with L and (-∆)α/2b ∈ Ln/α(Rn). In this article, we prove that the commutator[b, Lα/2] is bounded from the homogenous Sobolev space Lα2 (Rn) to L2(Rn).
Wenyu TAO
,
Yanping CHEN
,
Jili LI
. GRADIENT ESTIMATES FOR THE COMMUTATOR WITH FRACTIONAL DIFFERENTIATION FOR SECOND ORDER ELLIPTIC OPERATORS[J]. Acta mathematica scientia, Series B, 2019
, 39(5)
: 1255
-1264
.
DOI: 10.1007/s10473-019-0505-y
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