scholarly journals Sharp function estimates and boundedness for Toeplitz type operator related to general singular integral operator

2013 ◽  
Vol 14 (1) ◽  
pp. 159
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Type Operator ◽  
Sharp Function ◽  
Toeplitz Type Operator

scholarly journals Sharp function inequalities and boundness for Toeplitz type operator related to general fractional singular integral operator

2012 ◽  
Vol 92 (106) ◽  
pp. 165-176 ◽  
Author(s):  
Chuangxia Huang ◽  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Maximal Function ◽  
Type Operator ◽  
Sharp Maximal Function ◽  
Sharp Function ◽  
Toeplitz Type Operator

We establish some sharp maximal function inequalities for the Toeplitz type operator, which is related to certain fractional singular integral operator with general kernel. These results are helpful to investigate the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces respectively.

scholarly journals Weighted boundedness for toeplitz type operators associated to singular integral operator with non-smooth kernel

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2489-2502
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Maximal Function ◽  
Type Operator ◽  
Sharp Maximal Function ◽  
Lebesgue Spaces ◽  
Smooth Kernel ◽  
Toeplitz Type Operator

In this paper, the weighted boundedness of the Toeplitz type operator associated to some singular integral operator with non-smooth kernel on Lebesgue spaces are obtained. To do this, some weighted sharp maximal function inequalities for the operator are proved.

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