scholarly journals Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Pu Zhang ◽  
Daiqing Zhang
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Lipschitz Condition ◽  
Singular Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Multilinear Commutator

LetTbe a singular integral operator with its kernel satisfying|K(x-y)-∑k=1ℓ‍Bk(x)ϕk(y)|≤C|y|γ/|x-y|n+γ,|x|>2|y|>0, whereBkandϕk  (k=1,…,ℓ)are appropriate functions andγandCare positive constants. Forb→=(b1,…,bm)withbj∈BMO(ℝn), the multilinear commutatorTb→generated byTandb→is formally defined byTb→f(x)=∫ℝn∏j=1m‍(bj(x)-bj(y))K(x,y)f(y)dy. In this paper, the weightedLp-boundedness and the weighted weak typeLlog⁡Lestimate for the multilinear commutatorTb→are established.

scholarly journals Estimates of multilinear singular integral operators and mean oscillation

2014 ◽  
Vol 95 (109) ◽  
pp. 201-214
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Lebesgue Spaces ◽  
Marcinkiewicz Operator ◽  
Mean Oscillation

We prove the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces. The operators include Calder?n-Zygmund singular integral operator, Littlewood-Paley operator and Marcinkiewicz operator.

scholarly journals Boundedness of Singular Integral Operators with Variable Kernels on Weighted Weak Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hua Wang
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Variable Kernel ◽  
Decomposition Theory

Let TΩ be the singular integral operator with variable kernel Ω(x,z). In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of TΩ on these spaces, under some Dini type conditions imposed on the variable kernel Ω(x,z).

Estimates for maximal singular integral operators in non-homogeneous spaces

2006 ◽  
Vol 136 (2) ◽  
pp. 351-364 ◽  
Author(s):  
Guoen Hu ◽  
Yan Meng ◽  
Dachun Yang
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Homogeneous Spaces ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Standard Size ◽  
Hörmander Condition ◽  
Size Condition ◽  
Maximal Singular Integral

Under the assumption that the Radon measure μ on Rd satisfies only some growth condition, the authors prove that, for the maximal singular integral operator associated with a singular integral whose kernel only satisfies a standard size condition and the Hörmander condition, its boundedness in Lebesgue spaces Lp(μ) for any p ∈ (1, ∞) is equivalent to its boundedness from L1(μ) into weak L1(μ). As an application, the authors verify that if the truncated singular integral operators are bounded on L2(μ) uniformly, then the associated maximal singular integral operator is also bounded on Lp(μ) for any p ∈ (1, ∞).

scholarly journals The Boundedness of Commutators of Singular Integral Operators with Besov Functions

2010 ◽  
Vol 8 (3) ◽  
pp. 245-256
Author(s):  
Xionglue Gao ◽  
Bolin Ma
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators

In this paper, we prove the boundedness of commutator generated by singular integral operator and Besov function from someLdto Triebel-Lizorkin spaces.

On the Commutators of Singular Integral Operators with Rough Convolution Kernels

2016 ◽  
Vol 68 (4) ◽  
pp. 816-840
Author(s):  
Xiaoli Guo ◽  
Guoen Hu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Maximal Operator ◽  
Integral Operators ◽  
Mean Value ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Degree Zero ◽  
Convolution Kernels

AbstractLet TΩ be the singular integral operator with kernel , where Ω is homogeneous of degree zero, has mean value zero, and belongs to Lq(Sn–1) for some q ∊ (1,∞). In this paper, the authors establish the compactness on weighted Lp spaces and the Morrey spaces, for the commutator generated by CMO(ℝn) function and TΩ. The associated maximal operator and the discrete maximal operator are also considered.

scholarly journals Multilinear strongly singular integral operators with generalized kernels and applications

2021 ◽  
Vol 6 (12) ◽  
pp. 13533-13551
Author(s):  
Shuhui Yang ◽  
◽  
Yan Lin
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces

<abstract><p>In this paper, the authors study the boundedness properties of a class of multilinear strongly singular integral operator with generalized kernels on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces, respectively. Moreover, the types $ L^{\infty}\times \dots \times L^{\infty}\rightarrow BMO $ and $ BMO\times \dots \times BMO\rightarrow BMO $ endpoint estimates are also obtained.</p></abstract>

scholarly journals Continuity for some multilinear operators of integral operators on Triebel-Lizorkin spaces

2004 ◽  
Vol 2004 (38) ◽  
pp. 2039-2047
Author(s):  
Liu Lanzhe
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Fractional Integral Operator ◽  
Multilinear Operators

The continuityfor some multilinear operators related to certain fractional singular integral operators on Triebel-Lizorkin spaces is obtained. The operators include Calderon-Zygmund singular integral operator and fractional integral operator.

scholarly journals Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Guoen Hu ◽  
Haibo Lin ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Operator ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Littlewood Maximal Operator

WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

Sign in / Sign up

Export Citation Format

Share Document