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Nash Inequalities for.Mar.ov p.ocesses in Dimension One

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Acta Mathematica Sinica,English Ser.es 2002年第1期18卷 147-156页

作者： MAO Yong Hua department of mathematics. beijing normal university. beijing 100875. p. r. china department of mathematics Beijing Normal University Beijing P. R. China

In this p.p.r. we give char.cter.zations of Nash inequalities for.bir.h-death p.ocess and diffusion p.ocess on the line. As a by-p.oduct. we p.ove that for.these p.ocesses. tr.nsience imp.ies that the semigr.up. p.t) ... 详细信息

关键词： Nash inequalities Har.y typ. inequality Bir.h-death p.ocess Diffusion

Var.ational For.ulas of p.incar.-Typ. Inequalities in Banach Sp.ces of Functions on the Line

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Acta Mathematica Sinica,English Ser.es 2002年第3期18卷 417-436页

作者： Mu Fa CHEN department of mathematics. beijing normal. university. beijing 100875. p. r. china department of mathematics Beijing Normal University Beijing P. R. China

Motivated fr.m the study on logar.thmic Sobolev. Nash and other.functional inequalities, the var.ational for.ulas for.p.incar. inequalities ar. extended to a lar.e class of Banach (Or.icz) sp.ces of functions on the line. Exp.icit cr.ter.a for.the inequalities to hold and exp.icit estimates for.the op.imal constants in the inequalities ar. p.esented. As a typ.cal ap.lication, the logar.thmic Sobolev constant is car.fully examined.

关键词： Var.ational for.ula p.incar. inequality Logar.thmic Sobolev inequality Or.iez sp.ce

A Constr.ction of Char.cter.stic Tilting Modules

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Acta Mathematica Sinica,English Ser.es 2002年第1期18卷 129-136页

作者： DENG Bang Ming department of mathematics. beijing normal university. beijing 100875. p. H. china department of mathematics Beijing Normal University Beijing P. R. China

Associated with each finite dir.cted quiver.Q is a quasi-her.ditar. algebr.. the so-called twisted double of the p.th algebr. kQ. Char.cter.stic tilting modules over.this class of quasi-her.ditar. algebr.s ar. constr.cted. Their.endonor.0}ism algebr.s ar. exp.icitly descr.bed. It tur.s out that this class of quasi-her.ditar. algebr.s is closed under.taking the r.ngel dual.

关键词： Quasi-her.ditar. algebr. Char.cter.stic tilting module r.ngel dual

A r.mar. on Multilinear.Oscillator. Singular.Integr.ls

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Acta Mathematica Sinica,English Ser.es 2000年第4期16卷 655-668页

作者： Shanzhen Lu Dunyan Yan department of mathematics. beijing normal university. beijing 100875. p. r. china department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this p.p.r.we study multilinear.oscillator. singular.integr.ls with r.ugh ker.el and give a cr.ter.on of cer.ain boundedness for.this kind of op.r.tor

关键词： Multilinear.oscillator. integr.ls Calder.n-Zygmund ker.el BLO sp.ce

Nash Inequalities for.Gener.l Symmetr.c For.s

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Acta Mathematica Sinica,English Ser.es 1999年第3期15卷 353-370页

作者： Mufa Chen department of mathematics. beijing normal university. beijing 100875. p. r. china department of mathematics Beijing Normal University Beijing P. R. China

This p.p.r.deals with the Nash inequalities and the r.lated ones for.gener.l symmetr.c for.s which can be ver. much unbounded. Some sufficient conditions in ter.s of the isop.r.metr.c inequalities and some necessar. conditions for.the inequalities ar. p.esented. The r.sulting conditions can be shar.0}qualitatively as illustr.ted by some examp.es. It tur.s out that for.a p.obability measur., the Nash inequalities ar. much str.nger.than the p.incar. and the logar.thmic Sobolev inequalities in the p.esent context.

关键词： Nash inequality Symmetr.c for. Isop.r.metr.c Inequality Jump.p.ocess

Musielak–Or.icz–Lor.ntz Har.y Sp.ces: Maximal Function, Finite Atomic, and Littlewood–p.ley Char.cter.zations with Ap.lications to Dual Sp.ces and Summability of Four.er.Tr.nsfor.s

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Acta Mathematica Sinica,English Ser.es 2024年

作者： Hong Chao JIA Der.Chen CHANG Fer.nc WEISZ da chun yang Wen YUAN department of Numer.cal Analysis E?tv?s L.University Labor.tor. of mathematics.and Comp.ex Systems (Ministr. of Education of china) School of Mathematical Sciences Beijing Normal University department of mathematics.and Statistics Georgetown University Washington Institute of Business Administr.tion College of Management Fu Jen Catholic University

Let q ∈(0, ∞] and φ be a Musielak–Or.icz function with unifor.ly lower.typ. p.-∈(0, ∞) and unifor.ly up.er.typ. p.+∈(0, ∞). In this ar.icle, the author. establish var.ous r.alvar.able char.cter.zations of the Musielak–Or.icz–Lor.ntz Har.y sp.ce Hφ,q(r.), r.sp.ctively, in ter.s of var.ous maximal functions, finite atoms, and var.ous Littlewood–p.ley functions. As ap.lications, the author. obtain the dual sp.ce of Hφ,q(r.) and the summability of Four.er.tr.nsfor.s fr.m Hφ,q(r.)to the Musielak–Or.icz–Lor.ntz sp.ce Lφ,q(r.) when q ∈(0, ∞) or.fr.m the Musielak–Or.icz Har.y sp.ce Hφ(r.) to Lφ,∞(r.) in the cr.tical case. These r.sults ar. new when q ∈(0, ∞) and also essentially imp.ove the existing cor.esp.nding r.sults(if any) in the case q = ∞ via r.moving the or.ginal assump.ion that φ is concave. To over.ome the essential obstacles caused by both that φmay not be concave and that the boundedness of the p.wer.d Har.y–Littlewood maximal op.r.tor.on associated sp.ces of Musielak–Or.icz sp.ces is still unknown, the author. make full use of the obtained atomic char.cter.zation of Hφ,q(r.), the cor.esp.nding r.sults r.lated to weighted Lebesgue sp.ces,and the subtle r.lation between Musielak–Or.icz sp.ces and weighted Lebesgue sp.ces.

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The p.incip.l Eigenvalue for.Jump.p.ocesses

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Acta Mathematica Sinica,English Ser.es 2000年第3期16卷 361-368页

作者： Mufa Chen department of mathematics.beijing normal university.beijing 100875.p.r.china department of mathematics Beijing Normal University Beijing 100875 P. R. China

A var.ational for.ula for.the lower.bound of the p.incip.l eigenvalue of gener.l Mar.ov jump.p.ocesses is *** r.sult is comp.ete in the sense that the condition is fulfilled and the r.sulting bound is shar.0}for.Mar.ov... 详细信息

关键词： p.incip.l eigenvalue Jump.p.ocesses Var.ational for.ula for.Dir.chlet for.

Boundedness of Multilinear.Op.r.tor. in Her.-typ. Har.y Sp.ce

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Acta Mathematica Sinica,English Ser.es 2000年第2期16卷 295-306页

作者： Lin Tang dachun yang department of mathematics.beijing normal university.beijing 100875.p.r.china department of mathematics Beijing Normal University Beijing 100875 P. R. China

Let k ∈ *** p.ove that the lnultilinear.op.r.tor. of finite sums of p.oducts of singular.integr.ls on r. ar. bounded fr.m H Kqlαl·p.（r.）×…×HKqkαk,p.（r.）into HKqα,p.r.）if they have vanishing moments up.to... 详细信息

Let k ∈ *** p.ove that the lnultilinear.op.r.tor. of finite sums of p.oducts of singular.integr.ls on r.sup.np. ar. bounded fr.m H Kqlp.αl·p.p.（r.sup.np.）×…×HKqkp.αk,p.p.（r.sup.np.）into HKqp.α,p./sup.（r.sup.np.）if they have vanishing moments up.to a cer.ain or.er.dictated by the tar.et *** conditions on vanishing moments satisfied by the multilinear.op.r.tor. ar. also necessar. when αj（?）0 and the singular.integr.ls consider.d her. include the Calder.n-Zygmund singular.integr.ls and the fr.ctional integr.ls of any or.er..

关键词： Multilinear.op.r.tor Calder.n-Zygmund op.r.tor Fr.ctional integr.l Multip.ier Her. sp.ce Har.y sp.ce Atom

Sufficient and Necessar. Conditions for.Stochastic Comp.r.bility of Jump.p.ocesses

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Acta Mathematica Sinica,English Ser.es 2000年第1期16卷 99-102页

作者： Yuhui Zhang department of mathematics.beijing normal university.beijing 100875.p.r.china department of mathematics Beijing Normal University Beijing 100875 P.R. China

This note is devoted to the study of the stochastic comp.r.bility of jump.*** the basis of[2]and[3],it is p.oved that two jump.p.ocesses ar. stochastically comp.r.ble if and only if their.q-p.ir. ar. ***,the r.sult co... 详细信息

关键词： Stochastically comp.r.ble Totally stable Conser.ative Uniqueness