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Littlewood-p.ley op.r.tor. with var.able ker.els

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Science china mathematics 2006年第5期49卷 639-650页

作者： CHEN Jiecheng, ding yong & fan dashan department of mathematics, Zhejiang university (Xixi Camp.s), Hangzhou 310028, china School of Mathematical Sciences, beijing normal university, beijing 100875, china department of mathematics, university of wisconsin-milwaukee. milwaukee.WI 53201, usa department of mathematics, Centr.l china normal university, Wuhan 430074, china department of mathematics Zhejiang University [Xixi Camp.s] Hangzhou 310028 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI 53201 USA department of mathematics Central China Normal University Wuhan 430074 China

In this p.p.r.we study a cer.ain dir.ctional Hilber. tr.nsfor. and the boundedness on some mixed nor. sp.ces. As one of ap.lications, we p.ove the Lp.boundedness of the Littlewood-p.ley op.r.tor. with var.able ker.els... 详细信息

关键词： dir.ctional Hilber. tr.nsfor., Sobolev sp.ces, Littlewood-p.ley op.r.tor.var.able ker.el.

Weighted Boundedness for.a Class of r.ugh Multilinear.Op.r.tor.

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Acta Mathematica Sinica,English Ser.es 2001年第3期17卷 517-526页

作者： yong ding Shan Zhen LU department of mathematics,beijing normal university,beijing 100875,p.r.china E-mail:dingy@*** lusz@*** department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this p.p.r.we give the (L^p.ω~p.,L^q(ω~q)) boundedness for.a class of multilinear.op.r.tor., which is similar.to the higher.or.er.commutator.for.the r.ugh fr.ctional *** our.r.sults the ker.el function is mer.ly ... 详细信息

关键词： Multilinear.op.r.tor Fr.ctional integr.l r.ugh ker.el BMO A(p.q) weight

Weighted weak typ. estimates for.commutator. of the Mar.inkiewicz integr.ls

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Science china mathematics 2004年第1期47卷 83-95页

作者： ding yong, LU Shanzhen & ZHANG p.department of mathematics, beijing normal university, beijing 100875, china department of Infor.ation and Comp.ting Science, Zhejiang Institute of Science and Technology, Hangzhou 310033, china 1. department of mathematics Beijing Normal University 100875 Beijing China 2. department of Infor.ation and Comp.ting Science Zhejiang Institute of Science and Technology 310033 Hangzhou China

In this p.p.r.the author. give the weighted weak LlogL typ. estimates for.a class of the higher.or.er.commutator.gener.ted by the Mar.inkiewicz integr.l and a BMO function. In addition, the weak typ. nor. inequalities... 详细信息

关键词： Mar.inkiewicz integr.l, commutator. Ap weight, weak typ. estimate.

Continuity of Higher.Or.er.Commutator. on Cer.ain Har.y Sp.ces

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Acta Mathematica Sinica,English Ser.es 2002年第2期18卷 391-404页

作者： ding yong LU Shan Zhen department of mathematics,beijing normal university,beijing 100875.p.r.china E-mail:dingy@*** lusz@***ZHANG p. department of mathematics.Zhejiang university(at Xixi Camp.s).Hangzhou 310028,p.r.china,E-mail:zhp.j@263,net department of mathematics Beijing Normal University Beijing P.R. China department of mathematics Zhejiang University (at Xixi Campus) Hangzhou P.R. China

In this *** author. study the continuity p.op.r.ies of higher.or.er.commutator. gener.ted by the homogeneous fr.ctional integr.l and BMO functions on cer.ain Har.y sp.ces,weak Har.y sp.ces and Her.-typ. Har.y sp.ces.

关键词： Fr.ctional integr.l Homogeneous ker.el L^r.Dini condition Har.y sp.ce Her.-typ. Har.y sp.ce

Comp.ctness of the commutator. of p.r.bolic singular.integr.ls

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Science china mathematics 2010年第10期53卷 2633-2648页

作者： CHEN Yanp.ng1 & ding yong2,3 1department of mathematics and Mechanics,university of Science and Technology beijing,beijing 100083,china 2School of Mathematical Science,beijing normal university,beijing 100875,china 3Labor.tor. of mathematics and Comp.ex Systems (BNU),Ministr. of Education of china,beijing 100875,china 1. department of mathematics and Mechanics University of Science and Technology Beijing Beijing 100083 China2. School of Mathematical Science Beijing Normal University Beijing 100875 China3. Laboratory of Mathematics and Complex Systems (BNU) Ministry of Education of China Beijing 100875 China

In this p.p.r.the author. p.ove that the commutator.[b,T] of the p.r.bolic singular.integr.ls is a comp.ct op.r.tor.on Lp.r.)(1 < p.< ∞) if and only if b ∈ VMO(r.,ρ).The r.sult is substantial imp.ovement and extens... 详细信息

In this p.p.r.the author. p.ove that the commutator.[b,T] of the p.r.bolic singular.integr.ls is a comp.ct op.r.tor.on Lp.r.)(1 p.r.,ρ).The r.sult is substantial imp.ovement and extension of some known r.sults.

关键词： p.r.bolic singular integr.ls commutator. comp.ctness BMO VMO

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高阶交换子在Har.y空间上的连续性

数学学报（中文版） 2005年第1期48卷 191-200页

作者：丁勇陆善镇张璞北京师范大学数学系北京100875 浙江工程学院信息与计算科学系杭州310018

本文研究了由齐性分数次积分和BMO函数生成的高阶交换子在某些Har.y空间、弱Har.y空间和Her.型Har.y空间上的连续性.

关键词： Her.型Har.y空间高阶交换子连续性分数次积分 BMO函数弱Har.y空间生成

Weakly Str.ngly Singular.Integr.l Op.r.tor. on Anisotr.p.c Har.y Sp.ces and Their.Dual Op.r.tor.

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Acta Mathematica Sinica,English Ser.es 2009年第11期25卷 1849-1864页

作者： yong ding Sen Hua LAN School of Mathematical Sciences Laboratory of Mathematics and Complex Systems (BNU) Ministry of Education China Beijing Normal University Beijing 100875 P. R. China department of mathematics Lishui University Lishui 323000 P. R. China

Let A be an expansive dilation. We define weakly str.ngly singular.integr.l ker.els and study the action of the op.r.tor. induced by these ker.els on anisotr.p.c Har.y sp.ces associated with A.

关键词： anisotr.p.c Har.y sp.ce weakly str.ngly singular.op.r.tor atom molecule

Multi-p.r.meter.Tr.ebel-Lizor.in and Besov Sp.ces Associated with Flag Singular.Integr.ls

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Acta Mathematica Sinica,English Ser.es 2010年第4期26卷 603-620页

作者： yong ding Guo Zhen LU Bo Lin MA Labor.tor. of mathematics and Comp.ex Systems ( BNU) Ministry of Education P. R. China School of mathematics Beijing Normal University Beijing 100875 P. R. China department of mathematics Wayne State University Detroit 48202 USA College of mathematics and Infor.ation Engineer.ng Jiaxing University Jiaxing 314001 P. R. China

Though the theor. of one-p.r.meter.Tr.ebel-Lizor.in and Besov sp.ces has been ver. well develop.d in the p.st decades, the multi-p.r.meter.counter.0}r. of such a theor. is still absent. The main p.r.0}se of this p.p.r.is to develop.a theor. of multi-p.r.meter.Tr.ebel-Lizor.in and Besov sp.ces using the discr.te Littlewood-p.ley-Stein analysis in the setting of imp.icit multi-p.r.meter.str.ctur.. It is motivated by the r.cent wor. of Han and Lu in which they established a satisfactor. theor. of multi-p.r.meter.Littlewood-p.ley-Stein analysis and Har.y sp.ces associated with the flag singular.integr.l op.r.tor. studied by Muller.r.cci-Stein and Nagel-r.cci-Stein. We also p.ove the boundedness of flag singular.integr.l op.r.tor. on Tr.ebel-Lizor.in sp.ce and Besov sp.ce. Our.methods her. can be ap.lied to develop.easily the theor. of multi-p.r.meter.Tr.ebel-Lizor.in and Besov sp.ces in the p.r. p.oduct setting.

关键词： flag singular.integr.ls multip.r.meter.Tr.ebel-Lizor.in sp.ces discr.te Calder.n r.p.o- ducing for.ulas discr.te Littlewood-p.ley-Stein analysis

New Har.y Sp.ces Associated with Some Anisotr.p.c Her. Sp.ces and Their.Ap.lications

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Acta Mathematica Sinica,English Ser.es 2008年第9期24卷 1449-1470页

作者： yong ding Sen Hua Lan Shan Zhen Lu School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems (BNU) Ministry of Education Beijing 100875 P. R. China department of mathematics Lishui University Lishui 323000 P. R. China

In this p.p.r. a class of anisotr.p.c Her.-typ. Har.y sp.ces associated with a non-isotr.p.c dilation on ℝ n ar. intr.duced, and the centr.l atomic and molecular.decomp.sition char.cter.zations of those sp.ces ar. est... 详细信息

In this p.p.r. a class of anisotr.p.c Her.-typ. Har.y sp.ces associated with a non-isotr.p.c dilation on ℝp. n p.ar. intr.duced, and the centr.l atomic and molecular.decomp.sition char.cter.zations of those sp.ces ar. established. As some ap.lications of the decomp.sition theor., the author. study the inter.0}lation p.oblem and the boundedness of the centr.l δ-Calder.n-Zygmund op.r.tor. on the anisotr.p.c Her.-typ. Har.y sp.ces.

关键词： anisotr.p.c Har.y sp.ce anisotr.p.c Her.-typ. Har.y sp.ce centr.l atom centr.l molecule δ -Calder.n-Zygmund op.r.tor