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2005年10月11日

【期刊论文】Weak estimates for commutators of fractional integral operators

陆善镇， DING Yong (丁勇)， LU Shanzhen (陆善镇) & ZHANG Pu (张璞)

SCIENCE IN CHINA（Series A), 2002, 45(2):196-213，-0001，（）：

-1年11月30日

By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function, the weak type Llog Lestimates for the commutators of the fractional integral operator and the related maximal operator are established.

fractional integral,， commutator,， sharp function,， Young function,， Luxemburg norm.，

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2005年10月11日

【期刊论文】LP-boundedness of multilinear oscillatory singular integrals with Calder

陆善镇， LU Shanzhen (陆善镇) & YAN Dunyan (燕敦验)

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 131, Number 2, Pager 467-477，-0001，（）：

-1年11月30日

摘要

LP-boundedness is obtained for a class of multilinear oscillatory singular integrals with Calder

multilinear oscillatory integrals,， Calderon-Zygmund kernel,， BMO space.，

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2005年10月11日

【期刊论文】Lipschitz estimates for generalized commutators of fractional integrals

陆善镇， Shanzhen Lu* and Pu Zhang**

Math. Nachr. 252, 70-85(2003)，-0001，（）：

-1年11月30日

摘要

Let TAΩα ( θ<α<n) be the generalized commutator generatedby fractional intergral with rough kernal and the m-th order remaindr of the Taylor formual of a funcion A. In this paper, the (Lp\Lr) (r>1) bound edness, the weak (L1, Ln/(n-α-β) boundedness and the (Lp, Fβp,∞) boundednessof TAΩ1α are discussed, when D'A belongs to the Lipschitz funcion spaces.

Fractional maximal operator,， generalized commutator,， Lipschitx space,， Triebel-Lizorkin space

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2005年10月11日

【期刊论文】A CLASS OF MULT1LINEAR OSCILLATORY SINGULAR INTEGRALS RELATED TO BLOCK SPACES

陆善镇， SHANZHEN LU AND HUOXIONG WU

Tohoku Math. J. 56 (2004). 299-315，-0001，（）：

-1年11月30日

摘要

This paper is devoted to the study on the LP -mapping prnperlies for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel By means of the method of block decomposition tot the kernel funcion. the authors show that for any non trivial polynomial phase, the Lp(Rn) boundedness of the muhilinear oseillatory singular integral operators and that of the corresponding local multilinear singular integral opterators are equivalent; and for any real-valued polynomial phase, the Lp(Rn) bonundedness of the multi linear oscillatory integral operators can be deduced from that of the cprresponding multilinear singular integral operators.

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2005年10月11日

【期刊论文】Two-weight Weak type Norm Inequalities for the Commutators of Fractional Integrals

陆善镇， Zongguang Liu and Shanzhen Lu

Integr. Equ. Oper. Theory 48(2004),397-409，-0001，（）：

-1年11月30日

摘要

In this paper, we obtain a suffcient condition for two-weight weak type norm inequality for the commutators of fractional integral [b, Iα], where b∈BMO and 0<a<n.

Fractional integral,， Commutator.， Weight,， Weak type norln inequaliLy,， BMO

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