The boundedness of the Cauchy singular integral operator in weighted Besov type spaces with uniform norms

2002 ◽  
Vol 42 (1) ◽  
pp. 57-89 ◽  
Author(s):  
G. Mastroianni ◽  
M. G. Russo ◽  
W. Themistoclakis
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Type Spaces ◽  
Cauchy Singular Integral ◽  
Cauchy Singular Integral Operator ◽  
Besov Type 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.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

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