On commutators of fractional integrals
On commutators of fractional integrals
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DOI：
10.1090/s0002-9939-04-07437-4
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发表时间：
2004-07
期刊：
影响因子：
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通讯作者：
X. Duong;L. Yan
中科院分区：
文献类型：
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作者：
X. Duong;L. Yan
让L是一个解析半群的无穷小发电机L 2 (R n)与高斯内核,并让L -α/ 2 L的分数积分0 <α< n。蒙特利尔银行功能b (x) R n,我们展示了有界性的换向片[b, L -α/ 2](f) (x) = b (x) L -α/ 2 (f) (x) - L -α/ 2 (bf) (x) L p (R n) L q (R n),在1 < p < nα,1 = 1 p -αn。我们这有界性的结果仍然当R n取代李普希茨与无限域的R n测度。给出了磁性薛定谔算子和发散形式的二阶椭圆算子等一类微分算子的应用。
Let L be the infinitesimal generator of an analytic semigroup on L 2 (R n ) with Gaussian kernel bounds, and let L -α/2 be the fractional integrals of L for 0 < α < n. For a BMO function b(x) on R n , we show boundedness of the commutators [b, L -α/2 ](f)(x) = b(x)L -α/2 (f)(x) - L -α/2 (bf)(x) from L p (R n ) to L q (R n ), where 1 < p < n α, 1 q = 1 p - α n. Our result of this boundedness still holds when R n is replaced by a Lipschitz domain of R n with infinite measure. We give applications to large classes of differential operators such as the magnetic Schrodinger operators and second-order elliptic operators of divergence form.