Multilinear Calderon-Zygmund operators with kernels of Dini's type and applications

作者：Lu Guozhen; Zhang Pu^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2014, 107: 92-117.

DOI：10.1016/j.na.2014.05.005

• Multilinear Calderon-Zygmund operator
• Commutator
• Para-product
• Multilinear pseudo-differential operators
• Multiple weights
• Variable exponent Lebesgue spaces

The main purpose of this paper is to establish a number of results concerning boundedness of multi-linear Calderon-Zygmund operators with kernels of mild regularity. Let T be a multilinear Calderon-Zygmund operator of type omega(t) with omega being nondecreasing and omega is an element of Dini(1), but without assuming omega to be concave. We obtain the end-point weak-type estimates for multilinear operator T. The multiple-weighted norm inequalities for multilinear operator T and multilinear commutators of T with BMO functions are also established.
As applications, multiple-weighted norm estimates for para-products and bilinear pseudo-differential operators with mild regularity and their commutators are obtained.
Moreover, some boundedness properties of the multilinear operators are also established on variable exponent Lebesgue spaces.
Our results improve most of the earlier ones in the literature by removing the assumption of concavity of omega(t) and weakening the assumption of omega is an element of Dini(1/2) to omega is an element of Dini(1).

• 出版日期2014-9
• 单位牡丹江师范学院