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An endpoint estimate for maximal multilinear singular integral operators

Authors:

Yulan Jiao

Affiliation:

(1) School of Sciences, Information Engineering University, Zhengzhou, 450001, P. R. China

Abstract:

A weak type endpoint estimate for the maximal multilinear singular integral operator

$T_A^* f(x) = mathop {sup }limits_{varepsilon > 0} left| {int_{left| {x - y} right| > varepsilon } {frac{{Omega (x - y)}}{{left| {x - y} right|^{n + 1} }}(A(x) - A(y) - nabla A(y)(x - y))f(y)dy} } right|$

is established, where Θ is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO(ℝⁿ). A regularity condition on Θ which implies an LlogL type estimate of T _A ^* is given.

Keywords:

maximal multilinear singular integral operator bounded mean oscillation vanishing condition SINGULAR INTEGRAL OPERATORS MAXIMAL endpoint estimate regularity condition derivatives integrable the unit sphere moment order homogeneous of degree zero established weak type maximal singular integral operator

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