## Abstract

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 Schrödinger operators and second-order elliptic operators of divergence form.

Original language | English |
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Pages (from-to) | 3549-3557 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 132 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2004 |