scholarly journals Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights

2009 ◽  
Vol 7 (3) ◽  
pp. 301-311 ◽  
Author(s):  
Alexei Yu. Karlovich
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Sufficient Condition ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Partial Converse ◽  
Cauchy Singular Integral ◽  
Cauchy Singular Integral Operator

Recently V. Kokilashvili, N. Samko, and S. Samko have proved a sufficient condition for the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights over Carleson curves. This condition is formulated in terms of Matuszewska-Orlicz indices of weights. We prove a partial converse of their result.

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 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.

scholarly journals Banach algebra of the Fourier multipliers on weighted Banach function spaces

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Alexei Karlovich
Keyword(s):  
Integral Operator ◽  
Banach Algebra ◽  
Function Space ◽  
Singular Integral ◽  
Banach Function Space ◽  
Fourier Multipliers ◽  
Banach Function Spaces ◽  
Continuous Embedding ◽  
Cauchy Singular Integral ◽  
Cauchy Singular Integral Operator

AbstractLet MX,w(ℝ) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(ℝ,w).We prove that if the Cauchy singular integral operator S is bounded on X(ℝ, w), thenMX,w(ℝ) is continuously embedded into L∞(ℝ). An important consequence of the continuous embedding MX,w(ℝ) ⊂ L∞(ℝ) is that MX,w(ℝ) is a Banach algebra.

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