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 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).

Compact Commutators of Rough Singular Integral Operators

2015 ◽  
Vol 58 (1) ◽  
pp. 19-29 ◽  
Author(s):  
Jiecheng Chen ◽  
Guoen Hu
Keyword(s):  
Fourier Transform ◽  
Integral Operator ◽  
Singular Integral ◽  
Unit Sphere ◽  
Integral Operators ◽  
Mean Value ◽  
Degree Zero ◽  
Minimal Size ◽  
Smooth Kernels ◽  
Size Condition

AbstractLet b ∊ BMO(ℝn) and TΩ be the singular integral operator with kernel Ω(x)/|x|n, where Ω is homogeneous of degree zero, integrable, and has mean value zero on the unit sphere Sn-1. In this paper, using Fourier transform estimates and approximation to the operator TΩ by integral operators with smooth kernels, it is proved that if b ∊ CMO(ℝn) and satisfies certain minimal size condition, then the commutator generated by b and TΩ is a compact operator on Lp(ℝn) for appropriate index p. The associated maximal operator is also considered.

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 Φ-Admissible Sublinear Singular Operators and Generalized Orlicz-Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Javanshir J. Hasanov
Keyword(s):  
Integral Operator ◽  
Harmonic Analysis ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Maximal Operator ◽  
Morrey Spaces ◽  
Singular Operators ◽  
Littlewood Maximal Operator

We study the boundedness ofΦ-admissible sublinear singular operators on Orlicz-Morrey spacesMΦ,φℝn. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator and Calderón-Zygmund singular integral operator.

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.

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>

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