Boundedness of certain commutators on Triebel–Lizorkin spaces

In this paper, two types of commutators are considered, and the boundedness of these operators on Triebel–Lizorkin spaces are discussed.     

Borderline Weighted Estimates for Commutators of Fractional Integrals

Let $I_{\alpha,\vec{b}}$ be the multilinear commutators of the fractional integrals $I_{\alpha}$ with the symbol $\vec{b}=(b_1, \cdots,b_k )$. We show that the constant of borderline weighted estimates for $I_{\alpha}$ is $\frac{1}{{\varepsilon}}$, and for $I_{\alpha,{\vec{b}}}$ is $\frac{1}{{\varepsilon}^{k+1}}$ with each $b_i$ belongs to the Orlicz space $Osc_{\exp L^{s_i}}$.     

齐型空间上的T(1)定理和交换子

本文在齐型空间上讨论弱核形式的　Ｔ（１）　定理，　并得到弱核形式的奇异积分算子与　ＢＭＯ　函数的交换子的Ｌｐ有界性及端点估计　（１＜ｐ＜∞　）．     

Generalized Hörmander's conditions, commutators and weights

We present a general framework to deal with commutators of singular integral operators with BMO functions. Hörmander type conditions associated with Young functions are assumed on the kernels. Coifman type estimates, weighted norm inequalities and two-weight estimates are considered. We give applications to homogeneous singular integrals, Fourier multipliers and one-sided operators.     

Centers with degenerate infinity and their commutators

We study polynomial systems with degeneracy at infinity and a center-focus equilibrium at the origin. We give some general properties related to the existence of polynomial commutators and use these properties in order to characterize uniformly isochronous polynomial centers with polynomial commutator and, also, we show that the commutator of the centers of the analytic systems whose angular speed is constant can be chosen of radial form. Finally, we characterize the systems (−y+P_s+∑_j=kⁿ⁻¹xH_j,x+Q_s+∑_j=kⁿ⁻¹yH_j)^t with polynomial commutator, with P_j,Q_j,H_j and K_j homogeneous polynomials.     

Some new estimates for the commutators of n-dimensional Hausdorff operator

In this paper, we discuss the boundedness of commutators of high dimensional Hausdorff operator HΦ on Herz type spacesIn addition, central BMO estimates for such commutators are also presented.     

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.     

分数次积分的多线性换位子

设L是L2(Rn)上解析半群的无穷小生成算子,其积分核具有高斯界,L-α/2表示L的分数次积分算子,其中0＜α＜n.对自然数m,若bi(i=1,2,…,m)表示Rn上有界平均振荡函数,则由分数次积分L-α/2与bi(i=1,2,…,m)生成多线性交换子是从Lp(Rn)到Lq(Rn)是有界的,其中1＜p＜α/n,1/q=1/p-α/n.