scholarly journals Lipschitz Estimates for One-Sided Cohen’s Commutators on Weighted One-Sided Triebel-Lizorkin Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiao Jin Zhang ◽  
Xian Ming Hou
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Weighted Lebesgue Spaces ◽  
Lipschitz Estimates

We introduce one-sided Cohen’s commutators of singular integral operators and fractional integral operators, respectively. Using the extrapolation of one-sided weights, we establish the boundedness of these operators from weighted Lebesgue spaces to weighted one-sided Triebel-Lizorkin spaces.

scholarly journals Two-weight inequalities for singular integral operators satisfying a variant of Hörmander's condition

2009 ◽  
Vol 7 (1) ◽  
pp. 43-59 ◽  
Author(s):  
Vagif S. Guliyev
Keyword(s):  
Singular Integral ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Convolution Operators ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Hörmander’S Condition

In this paper, we present some sufficient conditions for the boundedness of convolution operators that their kernel satisfies a certain version of Hörmander's condition, in the weighted Lebesgue spacesLp,ω(ℝn).

scholarly journals On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Sha He ◽  
Xiangxing Tao
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Rough Kernels ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Maximal Singular Integral

We study some multilinear operators with rough kernels. For the multilinear fractional integral operatorsTΩ,αAand the multilinear fractional maximal integral operatorsMΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weightsLp,κ(u,v)whenDγA∈Λ˙β  (|γ|=m-1)orDγA∈BMO  (|γ|=m-1). For the multilinear singular integral operatorsTΩAand the multilinear maximal singular integral operatorsMΩA, we show they are bounded on weighted Morrey spaces with two weightsLp,κ(u,v)ifDγA∈Λ˙β  (|γ|=m-1)and bounded on weighted Morrey spaces with one weightLp,κ(w)ifDγA∈BMO  (|γ|=m-1)form=1,2.

Characterizations of bounded mean oscillation through commutators of bilinear singular integral operators

2016 ◽  
Vol 146 (6) ◽  
pp. 1159-1166 ◽  
Author(s):  
Lucas Chaffee
Keyword(s):  
Singular Integral ◽  
Wide Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Bounded Mean Oscillation ◽  
Fractional Integral Operators ◽  
Pointwise Multiplication ◽  
Bilinear Operators ◽  
Mean Oscillation

We characterize bounded mean oscillation in terms of the boundedness of commutators of various bilinear singular integral operators with pointwise multiplication. In particular, we study commutators of a wide class of bilinear operators of convolution type, including bilinear Calderón–Zygmund operators and the bilinear fractional integral operators.

scholarly journals Weighted Endpoint Estimates for Commutators of Singular Integral Operators on Orlicz-Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jinyun Qi ◽  
Hongxia Shi ◽  
Wenming Li
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Fractional Integral Operators

In this paper, we obtain the weighted endpoint estimates for the commutators of the singular integral operators with the BMO functions and the associated maximal operators on Orlicz-Morrey Spaces. We also get the similar results for the commutators of the fractional integral operators with the BMO functions and the associated maximal operators.

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 Boundedness of several operators on weighted Herz spaces

2009 ◽  
Vol 7 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Yasuo Komori ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Herz Space ◽  
Herz Spaces ◽  
Fractional Integral Operators

We consider the boundedness of singular integral operators and fractional integral operators on weighted Herz spaces. For this purpose we introduce generalized Herz space. Our results are the best possible.

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