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Commutators of singular integral operators satisfying a variant of a Lipschitz condition.


ABSTRACT: Let T be a singular integral operator with its kernel satisfying |K(x - y) - ∑(k=1)(ℓ) ‍Bk (x)ϕk(y)| ≤ C| y| (γ)/|x - y| (n+γ), |x | > 2| y| > 0, where B(k) and ϕk (k = 1,…, ℓ) are appropriate functions and γ and C are positive constants. For b = b1'...,bm) with bj ∈ BMO(ℝ(n)), the multilinear commutator Tb generated by T and b is formally defined by T(b)ƒ(x) = ∫(ℝn)[∏(j=1)(m) (b(j)(x) - b(j)(y))] K(x, y)ƒ(y)dy. In this paper, the weighted L(p)-boundedness and the weighted weak type L log estimate for the multilinear commutator T(b) are established.

SUBMITTER: Zhang P 

PROVIDER: S-EPMC4032734 | biostudies-other | 2014

REPOSITORIES: biostudies-other

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