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【期刊论文】Higher order commutators for a class of rough operators
陆善镇, Yong Ding aud Shanzhen Lu()
Ark. Mat., 37 (1999), 33-34,-0001,():
-1年11月30日
In this paper we study the (Lp(up, Lq(vq)) boundedness of the higher order commutators TmΩ,α, and MmΩ,α,b formed by the fractional integral operator TΩ,α, the fractinal maximal operator MΩ,α, and a function b (χ) in BMO(v), respectively. Our results improve and extend the corresponding results botained by Segovia and Torrea in 1993 [9].
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【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)
SIENCE IN CHINA (Series A), 2001, 44 (7): 877~888,-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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【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
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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【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
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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【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
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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