变指数加权Herz-Morrey空间上的分数次积分算子交换子的有界性

本文在指数函数的正则性自然假设下,建立了变指数加权Herz-Morrey空间上分数次积分算子及其交换子的有界性.从而得到了变指数加权Herz空间上的一个结果.     

Pseudodifferential Operators Approach to Singular Integral Operators in Weighted Variable Exponent Lebesgue Spaces on Carleson Curves

The main results of the paper are: (1) The boundedness of singular integral operators in the variable exponent Lebesgue spaces L ^p(·)(Γ, w) on a class of composed Carleson curves Γ where the weights w have a finite set of oscillating singularities. The proof of this result is based on the boundedness of Mellin pseudodifferential operators on the spaces L^p(·)(\mathbbR ₊,dm){L^{p(\cdot )}(\mathbb{R} _{+},d\mu)} where dμ is an invariant measure on multiplicative group ${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}. (2) Criterion of local invertibility of singular integral operators with piecewise slowly oscillating coefficients acting on L ^p(·)(Γ, w) spaces. We obtain this criterion from the corresponding criteria of local invertibility at the point 0 of Mellin pseudodifferential operators on \mathbbR₊{\mathbb{R}_{+}} and local invertibility of singular integral operators on \mathbbR{\mathbb{R}}. (3) Criterion of Fredholmness of singular integral operators in the variable exponent Lebesgue spaces L ^p(·)(Γ, w) where Γ belongs to a class of composed Carleson curves slowly oscillating at the nodes, and the weight w has a finite set of slowly oscillating singularities.     

Singular Integral Operators with Cauchy Kernel in Fractional Spaces

We single out the Besov spaces that embed into the class of continuous functions and enjoy the Fredholm theory of linear singular integral equations with Cauchy kernel. We give basic results of this theory in the class of continuous (rather than Holder continuous) functions in terms of Besov spaces. Alongside elliptic operators we consider violations of ellipticity: the degeneration of the symbol of an operator at finitely many points.     

Commutators Generated by Multilinear Calderon-Zygmund Type Singular Integral and Lipschitz Functions

In this paper,we establish the boundedness of commutators generated by the multilinear CalderonZygmud type singular integrals and Lipschitz functions on the Triebel-Lizorkin space and Lipschitz spaces.     

Singular Integral Operators with Fixed Singularities on Weighted Lebesgue Spaces

The paper is devoted to study of singular integral operators with fixed singularities at endpoints of contours on weighted Lebesgue spaces with general Muckenhoupt weights. Compactness of certain integral operators with fixed singularities is established. The membership of singular integral operators with fixed singularities to Banach algebras of singular integral operators on weighted Lebesgue spaces with slowly oscillating Muckenhoupt weights is proved on the basis of Balakrishnans formula from the theory of strongly continuous semi-groups of closed linear operators. Symbol calculus for such operators, Fredholm criteria and index formulas are obtained.     

Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Littlewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley g*λ-functions, is established on the Lebesgue spaces with variable exponent. Furthermore,the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.     

Fractional Type Integral Operators on Variable Hardy Spaces

Given certain n × n invertible matrices A ₁, . . . , A _m and 0 ≦ α < n, we obtain the \({H^{p(.)}(\mathbb{R}^n) \to L^{q(.)}(\mathbb{R}^n)}\) boundedness of the integral operator with kernel \({k(x, y) = |x - A_1y|^{-\alpha_1} . . . |x - A_my|^{-\alpha_m}}\) , where α ₁ +  . . . + α _m = n ? α and p(.), q(.) are exponent functions satisfying log-Hölder continuity conditions locally and at infinity related by \({\frac{1}{q(.)} = \frac{1}{p(.)} - \frac{\alpha}{n}}\) . We also obtain the \({H^{p(.)}(\mathbb{R}^n) \to H^{q(.)}(\mathbb{R}^n)}\) boundedness of the Riesz potential operator.     

强奇异积分算子的交换子在Hardy空间的连续性(英文)

设1p>n/(n δ/ε)和b∈BOM(Rn),本文证明了强奇异积分算子交换子的(Hpb,Lp)-型和(Hp,∞b,Lp,∞)-型有界性,其中Hpb和Hp,∞b分别为Hardy空间与弱Hardy空间的变形。     

有变量核的分数次积分算子交换子的CBMO估计(英文)

In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.     

The Commutators of Strongly Singular Integral Operators on the Weighted Hardy Spaces

Acta Mathematica Sinica, English Series - Let T be a strongly singular Calderón-Zygmund operator and b ∈ Lloc(ℝn). This article finds out a class of non-trivial subspaces...     

Calderon-Zygmund奇异积分算子交换子在Herz型Hardy空间中的有界性

本文证明了交换子[6,T]在一类Herz型Hardy空间中的强型与弱型有界性估计,其中6∈BMO(Rn),T为Calderon-zygmund奇异积分算子。     

CBMO Estimates for Commutators of Multilinear Fractional Integral Operators on Herz Spaces

The CBMO estimates for commutators of fractional integral and Multilinear fractional integral operators with rough kernel are established. This work was completed with the support of Hunan Provincial Natural Science Foundation of China 06A0074.     

Commutators of Lipschitz Functions and Singular Integrals with Non-Smooth Kernels on Euclidean Spaces

In this article, we obtain the L p-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.     

Commutators of Bilinear Pseudodifferential Operators and Lipschitz Functions

Commutators of bilinear pseudodifferential operators and the operation of multiplication by a Lipschitz function are studied. The bilinear symbols of the pseudodifferential operators considered belong to classes that are shown to properly contain certain bilinear Hörmander classes of symbols of order one. The corresponding commutators are proved to be bilinear Calderón–Zygmund operators.     

向量值奇异积分算子的交换子

本文分别讨 论了 Ｈａｒｄｙ Ｌｉｔｔｌｅｗ ｏｏｄ 极大 算子和奇 异积分算 子的交换 子在加权 Ｈｅｒｚ 空间 ,加权 Ｌｐ空间中的 有界性     

Lipschitz Functions and Fractional Sobolev Spaces

We consider a semi-group of Markovian and symmetric operators to which we associate fractional Sobolev spaces (0<<1 and 1p if p2. This holds in particular in the case of the Ornstein–Uhlenbeck semi-group on an abstract Wiener space. We also study fractional Sobolev spaces obtained by real interpolation.     

多线性分数次Hardy算子交换子的Lipschitz估计

主要在齐次Morrey-Herz空间MK_(p,q)~(α,λ)(R~n)上建立了由n维分数次Hardy算子和Lipschitz函数生成的多线性交换子H_(e,b)的有界性.     

Lipschitz Estimates for Commutators of $N$-Dimensional Fractional Hardy Operators

In this paper, it is proved that the commutator$\mathcal{H}_{β,b}$ which is generated by the $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ and $b\in \dot{Λ}_α(\mathbb{R}^n)$ is bounded from $L^P(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$, where $0<α<1,1相似文献