极大算子交换子在各向异性Morrey-Herz空间上的有界性

本文引进了伴随伸缩矩阵A的各向异性齐次Morrey-Herz型空间,利用Hardy-Littlewod极大算子交换子的Lp有界性,证明了Hardy-Littlewod极大算子交换子在各向异性齐次Morrey-Herz型空间上的有界性,对于分数次Hardy-Littlewod极大算子交换子也得到了类似的结果.     

位势算子与极大算子的加权有界性

本文考虑的算子,包括极大算子、分数次积分、poisson 算子,都是把 R~n 上的函数映到 R_ ~(n 1)上的函数的。主要结果有二个方面:首先解决了一个 Muckenhoupt 型问题,即,给出了 R 上的权函数ω(x)的充要条件,使得这些算子是从 L~p(R~n,ω(x))到某个加权 L~q(R_ ~(n 1))空间的有界算子;其次,建立了这些算子的一个因子分解。     

一类极大奇异积分算子的 L~p 有界性

作者对由 R Fefferman 引进的一类广义奇异积分建立了 L~p 有界性的某些结果.这类奇异积分的核是相当粗糙的.它取 (?)(t)h(t)/|t|~(?)的形式,其中 h为一有界的径向函数,而Ω属于某种由块生成的空间.     

沿旋转曲面奇异积分的有界性

本文建立了具有粗糙核的沿曲面奇异积分算子的L^P有界性．其中粗糙核K(y)=Ω（y)/|y|^n,y∈R^n以及曲面{(y，φ(|y|）)：y∈R^n)满足某种光滑条件．同时，相应极大算子的有界性也被得到.     

沿复合子簇的粗糙核极大算子

给出了两类相关于沿复合子簇的粗糙核奇异积分的极大算子的L~p有界性,本质上极大地改进和一般化了已有的结果.作为应用,相关的奇异积分,Marcinkiewicz积分和相应的极大算子的L~p有界性也被建立.     

加权BMO函数空间上的Hardy—Littlewood极大算子

本文给出了Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ极大函数的加权ＢＭＯ的有界性证明，即若ｆ∈ＢＭＯ，Ｗ∈Ａ∞且ｉｎｆｍｆ（ｘ）〈∞则Ｍ（ｆ）（ｚ）∈ＢＭＯ。     

粗糙平方函数及极大算子的弱型估计

§ 1　 PreliminariesWe considerψ( x)∈ L1 ( Rn) satisfying the mean valuezero,i.e.∫Rnψdx=0 ,and definethe square function g( f) on Rnbyg( f) ( x) =( k|ψk* f|2 ) 1 2 ( x)for f∈ S( Rn) ,the Schwartz space,whereψk( x) =ψ2 k( x) .　　 Whenψ has some smooth property,one can obtain the weak type estimate by viewingthe square function g( f) as the vector-valued singularintegrals,which the readercan referto [1 ,2 ] .As for the results aboutthe Lp-estimates,see [3,4 ] .In this paper,we sha…     

具广义Calderón-Zygmund核的多线性振荡奇异积分极大算子的有界性

本文研究了具有广义Calderon-Zygmund核的多线性奇异积分极大算子和多线性振荡奇异积分极 大算子,证明了这类极大算子的Lp-有界性．     

A Dual Criterion for Maximal Monotonicity of Composition Operators

In this paper we present a dual criterion for the maximal monotonicity of the composition operator , where is a maximal monotone (set-valued) operator and is a continuous linear map with the adjoint , and are reflexive Banach spaces, and the product notation indicates composition. The dual criterion is expressed in terms of the closure condition involving the epigraph of the conjugate of Fitzpatrick function associated with , and the operator As an easy application, a dual criterion for the maximality of the sum of two maximal monotone operators is also given. The work of this author was completed while at the School of Mathematics, University of New South Wales, Sydney, Australia.     

A Family of Enlargements of Maximal Monotone Operators

We introduce a family of enlargements of maximal monotone operators. The Brønsted and Rockafellar -subdifferential operator can be regarded as an enlargement of the subdifferential. The family of enlargements introduced in this paper generalizes the Brønsted and Rockafellar -subdifferential (enlargement) and also generalize the enlargement of an arbitrary maximal monotone operator recently proposed by Burachik, Iusem and Svaiter. We characterize the biggest and the smallest enlargement belonging to this family and discuss some general properties of its members. A subfamily is also studied, namely the subfamily of those enlargements which are also additive. Members of this subfamily are formally closer to the -subdifferential. Existence of maximal elements is proved. In the case of the subdifferential, we prove that the -subdifferential is maximal in this subfamily.     

Damped Oscillatory Integrals and Maximal Operators

In the present paper, we consider estimates of the Fourier transform of Borel measures concentrated on analytic hypersurfaces and containing a mitigating factor. The mitigating factors are expressed in terms of principal curvatures of the surface. The resulting estimates are applied to investigating the boundedness of the corresponding maximal operators.     

Spherical Maximal Operators on Radial Functions

Let A_tf(x) denote the mean of f over a sphere of radius t and center x. We prove sharp estimates for the maximal function M_E f(X) = sup_t∈_E |Atf(x)| where E is a fixed set in IR⁺ and f is a radial function ∈ L^p(IR^d). Let P_d = d/(d?1) (the critical exponent for Stein's maximal function). For the cases (i) p < p_d, d ? 2, and (ii) p = p_d, d ? 3, and for p ? q ? ∞ we prove necessary and sufficient conditions on E for M_E to map radial functions in L^p to the Lorentz space L^P,q.     

极大单调算子和非扩展映射的迭代收敛定理及其应用

In this paper, two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Two strong convergence theorems are obtained and their applications on finding the minimizer of a kind of convex functional are discussed, which extend some previous work.     

Characterization of a Two-Weighted Vector-Valued Inequality for Fractional Maximal Operators

We give a characterization of the weights u(·) and v(·) for which the fractional maximal operator M _s is bounded from the weighted Lebesgue spaces L ^p(l ^r, vdx) into L ^q(l ^r, udx) whenever 0 s < n, 1 < p, r < , and 1 q < .     

Maximal Monotone Operators, Convex Functions and a Special Family of Enlargements

This work establishes new connections between maximal monotone operators and convex functions. Associated to each maximal monotone operator, there is a family of convex functions, each of which characterizes the operator. The basic tool in our analysis is a family of enlargements, recently introduced by Svaiter. This family of convex functions is in a one-to-one relation with a subfamily of these enlargements. We study the family of convex functions, and determine its extremal elements. An operator closely related to the Legendre–Fenchel conjugacy is introduced and we prove that this family of convex functions is invariant under this operator. The particular case in which the operator is a subdifferential of a convex function is discussed.     

极大算子的加权BLO估计(英文)

引入加权BLO空间,得到了极大奇异积分算子和Hardy-Littlewood极大算子的加权BLO估计.     

Boundeness of a Class of Maximal Operators on H~p Spaces on Compact Lie Groups

In this paper we discuss the weak type(H^p,L^p) boundedness of a class of maximal operators T*^ψ and themaximal strong mean boundedness of a family of the operators ｛T^ψ｝ on the atomic H^p spaces on compact Lic groups.Also,we obtain the correspoding convergent results.     

The Sum and Chain Rules for Maximal Monotone Operators

This paper is primarily concerned with the problem of maximality for the sum A + B and composition L* ML in non-reflexive Banach space settings under qualifications constraints involving the domains of A, B, M. Here X, Y are Banach spaces with duals X*, Y*, A, B: X ⇉ X*, M: Y ⇉ Y* are multi-valued maximal monotone operators, and L: X → Y is linear bounded. Based on the Fitzpatrick function, new characterizations for the maximality of an operator as well as simpler proofs, improvements of previously known results, and several new results on the topic are presented.