Derivative Estimates of Semigroups and Riesz Transforms on Vector Bundles

We use versions of Bismut type derivative formulas obtained by Driver and Thalmaier [9], to prove derivative estimates for various heat semigroups on Riemannian vector bundles. As an application, the weak (1,1) property for a class of Riesz transforms on a vector bundle is established. Some concrete examples of vector bundles (e.g., differential forms) are considered to illustrate the results.     

由Schr?dinger算子定义的Riesz变换的Lp估计

本文主要讨论了当非负位势 V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x))+V(x)所定义的 Riesz变换在 L^p空间的有界性。     

Hp(Ωn)(0＜p＜1)上临界阶Riesz平均强求和的逼近

本文讨论了球面上Hardy空间Hp(0＜p＜1)中Riesz平均的强求和在临界阶δ=n/p-n+1/2的有界性,并且建立了它和最佳逼近之间的关系.     

Recognition of subgroups of direct products of hyperbolic groups

We give examples of direct products of three hyperbolic groups in which there cannot exist an algorithm to decide which finitely presented subgroups are isomorphic.

     

A characterization of an order ideal in Riesz spaces

In this paper we give a characterization of order ideals in Riesz spaces.

     

超格的商结构

通过引入超格的强闭集、上半补超格、数量上界单位元等概念,引出超格上的等价关系.构造数量上界单位集,在此基础上进一步研究超格的一些性质.商代数结构定理的建立对于完善超格的商结构具有实际意义.     

The bicompletion of an asymmetric normed linear space

A biBanach space is an asymmetric normed linear space (X,‖·‖) such that the normed linear space (X,‖·‖^s) is a Banach space, where ‖x‖^s= max {‖x‖,‖-x‖} for all x∈X. We prove that each asymmetric normed linear space (X,‖·‖) is isometrically isomorphic to a dense subspace of a biBanach space (Y,‖·‖_Y). Furthermore the space (Y,‖·‖_Y) is unique (up to isometric isomorphism). This revised version was published online in August 2006 with corrections to the Cover Date.     

ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

IPreliminarlesTheee。etOOk totot比OO。stsllCCdCSdO‘lOll‘。山OOqll时1OO/(。)＝。,SS山 SFSSdPoint Theorems[‘’,”],Degree Theory【9,15]．In general these are used when f aPPlies a set ora space on itself．Cm眈inn眈ion Methods can be used to test the existence ofa solution whenf pplies a set or a sp。e on it咖‘－’,”－“l,or aPPlies a set or sP。m another sP。,s。M see here．wrthermore,contlnuulon methods pve us the exlstence ofcurves wb讪 can beused to CalCttlue the Sdutionsl6…     

Linear rank and corank preserving maps on (H) and an application to *-semigroup isomorphisms of operator ideals

We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on B(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-1 non-increasing and rank-1 preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals.     

构造正交小波基的基本方法之一

本文不仅给出一种构造局部性好的正交小波基的方法,并且给出了构造各种优良性质的正交小波基的一般思想方法。其特点:使构造的小波母函数有具体的表达式,既有较好的光滑性,又有很好的局部性,并且其收敛速度与│t│~（-（3k 1））同阶,其中k为任意自然数。这种方法不需要每次重新构造函数,只要改变k的值,就能满足不同实际问题的需要。