Variation and oscillation inequalities for commutators in two-weight setting

2020 ◽  
Vol 32 (6) ◽  
pp. 1459-1475
Author(s):  
Yongming Wen ◽  
Weichao Guo ◽  
Huoxiong Wu
Keyword(s):  
Singular Integrals ◽  
Iterated Commutators

AbstractThis paper studies the two-weight estimates of variation and oscillation operators for commutators of singular integrals with weighted {\mathrm{BMO}} functions. A new characterization of weighted {\mathrm{BMO}} spaces via the boundedness of variation and oscillation operators for the iterated commutators of Calderón–Zygmund singular integrals in the two-weight setting is given.

scholarly journals Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianfeng Dong ◽  
Jizheng Huang ◽  
Heping Liu
Keyword(s):  
Molecular Characterization ◽  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Hardy Type ◽  
Type Spaces ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator onRn,n≥3, whereV≢0is a nonnegative potential belonging to the reverse Hölder classBn/2. The Hardy type spacesHLp, n/(n+δ) <p≤1,for someδ>0, are defined in terms of the maximal function with respect to the semigroup{e-tL}t>0. In this paper, we investigate the bounded properties of some singular integral operators related toL, such asLiγand∇L-1/2, on spacesHLp. We give the molecular characterization ofHLp, which is used to establish theHLp-boundedness of singular integrals.

scholarly journals End-point estimates for iterated commutators of multilinear singular integrals

2013 ◽  
Vol 46 (1) ◽  
pp. 26-42 ◽  
Author(s):  
Carlos Pérez ◽  
Gladis Pradolini ◽  
Rodolfo H. Torres ◽  
Rodrigo Trujillo-González
Keyword(s):  
Singular Integrals ◽  
End Point ◽  
Point Estimates ◽  
Iterated Commutators ◽  
Multilinear Singular Integrals

scholarly journals A charaterization of commutators for parabolic singular integrals

2011 ◽  
Vol 108 (1) ◽  
pp. 5
Author(s):  
Yanping Chen ◽  
Yong Ding
Keyword(s):  
Orlicz Space ◽  
Kernel Function ◽  
Unit Sphere ◽  
Singular Integrals ◽  
Bounded Operator ◽  
Parabolic Singular Integrals

In this paper, the authors give a characterization of the $L^p$-boundedness of the commutators for the parabolic singular integrals. More precisely, the authors prove that if $b\in \mathrm{BMO}_\varphi(\mathsf{R}^n,\rho)$, then the commutator $[b,T]$ is a bounded operator from $L^p(\mathsf{R}^n)$ to the Orlicz space $L_\psi(\mathsf{R}^n)$, where the kernel function $\Omega$ has no any smoothness on the unit sphere $S^{n-1}$. Conversely, if assuming on $\Omega$ a slight smoothness on $S^{n-1}$, then the boundedness of $[b,T]$ from $L^p(\mathsf{R}^n)$ to $L_\psi(\mathsf{R}^n)$ implies that $b\in \mathrm{BMO}_\varphi(\mathsf{R}^n,\rho)$. The results in this paper improve essentially and extend some known conclusions.

A Generalized Characterization of Commutators of Parabolic Singular Integrals

1999 ◽  
Vol 42 (4) ◽  
pp. 463-477 ◽  
Author(s):  
Steve Hofmann ◽  
Xinwei Li ◽  
Dachun Yang
Keyword(s):  
Singular Integrals ◽  
Cancellation Property ◽  
Parabolic Singular Integrals

AbstractLet and , where λ > 0 and . Denote . We characterize those functions A(x) for which the parabolic Calderón commutatoris bounded on L2(ℝn), where , K is smooth away fromthe origin and satisfies a certain cancellation property.

Sign in / Sign up

Export Citation Format

Share Document