scholarly journals Cauchy singular integral operator with parameters in Log-Hölder spaces

2021 ◽  
Author(s):  
Yifei Pan ◽  
Yuan Zhang
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Hölder Spaces ◽  
Cauchy Singular Integral ◽  
Cauchy Singular Integral Operator ◽  
Holder Spaces

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 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.

On a singular integral operator

1988 ◽  
Vol 43 (3) ◽  
pp. 199-200
Author(s):  
K Kh Boimatov ◽  
G Dzhangibekov
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral
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