相伴于非散度型椭圆算子的Riesz变换的L~p有界性

本文利用小波方法在一般阶的非散度椭圆算子的系数BMO模非常小的情形下,证明了广义 Riesz变换的 L~p(2≤p<+∞)有界性。     

Riesz Transforms Characterizations of Hardy Spaces $$H^1$$ for the Rational Dunkl Setting and Multidimensional Bessel Operators

We characterize the Hardy space \(H^1\) in the rational Dunkl setting associated with the reflection group \(\mathbb {Z}_2^n\) by means of special Riesz transforms. As a corollary we obtain Riesz transforms characterization of \(H^1\) for product of Bessel operators in \((0,\infty )^n\).     

Continuity for Maximal Multilinear Bochner-Riesz Operators on Hardy and Herz Hardy Spaces

Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ（｜α｜= m）, The continuity of the operator on some Hardy and Herz type Hardy is obtained.     

伴随Herz空间的Hardy空间上的向量值Calderón-Zygmund算子(英文)

本文证明了一类具有向量值核的Calderon－Zygmund算子是Herz型Hard,空间HKp到向量值Herz空间KE,p有界的,应用这一结果,得到了粗糙核Calderon－Zygmund算子,极大型Calderon－Zygmund算子,极大算子等是HKp到Kp有界的．     

Hardy空间的等价刻画

设Ｇ为局部域Ｋ上的２ｎ＋１维Ｈｅｉｓｅｎｂｅｒｇ群．本文证明了通过各种极大函数定义的Ｈａｒｄｙ空间的等价性，给出了Ｈａｒｄｙ空间的原子分解．利用这些等价定义及一些卷积算子定理，给出了Ｈａｒｄｙ空间的平方函数刻画——Ｌｕｚｉｎ面积函数刻画与Ｌｉｔｌｅｗｏｏｄ－Ｐａｌｅｙ平方函数刻画     

Hardy空间到Zygmund型空间的Riemann-Stieltjes算子

利用Hardy空间中函数的高阶导数的估计,通过构造一些新的检验函数,运用解析函数的性质与算子理论,给出了从Hardy空间到Zygmund型空间的Riemann—Stieltjes算子的有界性和紧性的特征,获得了若干个充要条件.     

Hardy and Carleson Measure Spaces Associated with Operators on Spaces of Homogeneous Type

Let (X, d, μ) be a metric measure space with doubling property. The Hardy spaces associated with operators L were introduced and studied by many authors. All these spaces, however, were first defined by L ²(X) functions and finally the Hardy spaces were formally defined by the closure of these subspaces of L ²(X) with respect to Hardy spaces norms. A natural and interesting question in this context is to characterize the closure. The purpose of this paper is to answer this question. More precisely, we will introduce \({CMO}_{L}^{p}(X)\), the Carleson measure spaces associated with operators L, and characterize the Hardy spaces associated with operators L via \(({CMO}_{L}^{p}(X))'\), the distributions of \({CMO}_{L}^{p}(X)\).     

四元数Hilbert空间中Riesz基的刻画*

四元数Hilbert空间在应用物理科学特别是量子物理中占有重要地位.本文讨论四元数Hilbert空间的框架理论, 在四元数Hilbert空间中引入了Riesz基的概念, 在此基础上刻画了Riesz基,给出了它们的一些等价条件; 特别地, 得到了四元数Hilbert空间中的一个序列是Riesz基的充要条件是它是一个具有双正交序列的完备Bessel序列,且它的双正交序列也是一个完备Bessel序列; 并进一步证明了双正交序列中一个序列的完备性可以从特征刻画中去除.文中举例说明了双正交性、完备性和Bessel性质之间的关系.     

Generalized Vanishing Mean Oscillation Spaces Associated with Divergence Form Elliptic Operators

Let L be a divergence form elliptic operator with complex bounded measurable coefficients, ω a positive concave function on (0, ∞) of strictly critical lower type p ω ∈(0, 1] and ρ(t) = t ?1/ω ?1(t ?1) for ${t\in (0,\infty).}Let L be a divergence form elliptic operator with complex bounded measurable coefficients, ω a positive concave function on (0, ∞) of strictly critical lower type p ω ∈(0, 1] and ρ(t) = t −1/ω −1(t −1) for t ? (0,￥).{t\in (0,\infty).} In this paper, the authors introduce the generalized VMO spaces VMOr, L(\mathbb Rn){{\mathop{\rm VMO}_ {\rho, L}({\mathbb R}^n)}} associated with L, and characterize them via tent spaces. As applications, the authors show that (VMOr,L (\mathbb Rn))*=Bw,L*(\mathbb Rn){({\rm VMO}_{\rho,L} ({\mathbb R}^n))^\ast=B_{\omega,L^\ast}({\mathbb R}^n)}, where L * denotes the adjoint operator of L in L2(\mathbb Rn){L^2({\mathbb R}^n)} and Bw,L*(\mathbb Rn){B_{\omega,L^\ast}({\mathbb R}^n)} the Banach completion of the Orlicz–Hardy space Hw,L*(\mathbb Rn){H_{\omega,L^\ast}({\mathbb R}^n)}. Notice that ω(t) = t p for all t ? (0,￥){t\in (0,\infty)} and p ? (0,1]{p\in (0,1]} is a typical example of positive concave functions satisfying the assumptions. In particular, when p = 1, then ρ(t) ≡ 1 and (VMO1, L(\mathbb Rn))*=HL*1(\mathbb Rn){({\mathop{\rm VMO}_{1, L}({\mathbb R}^n)})^\ast=H_{L^\ast}^1({\mathbb R}^n)}, where HL*1(\mathbb Rn){H_{L^\ast}^1({\mathbb R}^n)} was the Hardy space introduced by Hofmann and Mayboroda.     

Spectral Multipliers for Hardy Spaces Associated with Schrodinger Operators with Polynomial Potentials

Let T_t be the semigroup of linear operators generated by a Schrödingeroperator – A = – V, where V is a non-negative polynomial,and let be the spectral resolution of A. We say that f is an element of if the maximal function Mf(x) = sup_t>0|T_tf(x)| belongs toL_p. We prove a criterion of Mihlin type on functions F whichimplies boundedness of the operators on , 0 < p 1. 1991 MathematicsSubject Classification 42B30, 35J10.     

Hardy空间上的有界复合算子

本文讨论了由解析映射φ：Ｂｎ→Ｂｍ诱导复合算子的有界性；特别地，研究了由保测内映射诱导复合算子的性质．作为推论，得到了Ｗ．Ｒｕｄｉｎ［１０］中一个公开问题的解答．     

Hardy空间之间的加权复合算子

本文研究了复平面中单位圆盘D上不同Hardy空间之间的加权复合算子，利用Carleson测度的概念分别给出了有界或紧的加权复合算子的充分必要条件。本文也用角数的概念给出了紧加权复合算子的一个必要条件。     

球面Hardy空间上Riesz平均的逼近

引进了球面Hrady空间上Riesz平均算子及Peetre K模。讨论了Riesz平均算子在Hardy空间上的逼近性质。证明了Riesz平均算子与Peetre K模的强渐近等价关系。所得结果表明Peetre K模完全刻划了Riesz平均的逼近。     

Pseudodifferential Operators on Local Hardy Spaces

In this work, we study the continuity of pseudodifferential operators on local Hardy spaces h ^p (ℝ ⁿ ) and generalize the results due to Goldberg and Taylor by showing that operators with symbols in S _1,δ ⁰(ℝ ⁿ ), 0≤δ<1, and in some subclasses of S _1,1⁰(ℝ ⁿ ) are bounded on h ^p (ℝ ⁿ ) (0<p≤1). As an application, we study the local solvability of the planar vector field L=∂ _t +ib(x,t)∂ _x , b(x,t)≥0, in spaces of mixed norm involving Hardy spaces. Work supported in part by CNPq, FINEP, and FAPESP.     

Convolution Operators on Discrete Hardy Spaces

We establish the connection between the boundedness of convolution operators on H^p(ℝ^N) and some related operators on H^p(ℤ^N). The results we obtain here extend the already known for L^p spaces with p > 1. We also study similar results for maximal operators given by convolution with the dilation of a fixed kernel. Our main tools are some known results about functions of exponential type already presented in [BC1] that, in particular, allow us to prove a sampling theorem for functions of exponential type belonging to Hardy spaces     

从Hardy空间到Zygmund-型空间的加权微分复合算子

设φ为单位圆盘D上的解析自映射,H(D)表示D上的所有解析函数的集合,u∈H(D).研究了从Hardy空间到Zygmund-型空间及小Zygmund-型空间的加权微分复合算子D_(φ,u)~n,的有界性和紧性,其中n∈N_0.     

Disjointness Preserving Operators on Complex Riesz Spaces

It is proven that ifE and F are complex Riesz spaces and ifT is an order bounded disjointness preserving operator fromE intoF , then This fundamental result of M. Meyer is obtained by elementary means using as the main tool the functional calculus derived from the Freudenthal spectral theorem. It is also shown that ifT is an order bounded disjointness preserving operator, a formula of the form holds. It implies a polar decomposition of an order bounded disjointness preserving operator as the product of a Riesz homomorphism and an orthomorphism. Results of P. Meyer-Nieberg in this regard are generalized.     

Feller Semigroups Generated by Degenerate Elliptic Operators

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with sticky boundary condition on various spaces of continuous functions, generalizing the previous work. More precisely we construct Feller semigroups corresponding to such a diffusion phenomenon that a Markovian particle moves continuously in the state space, sticking to the boundary.