Boundedness of Weighted Singular Integral Operators on a Carleson Curve in Grand Lebesgue Spaces

2010 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Stefan Samko ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Grand Lebesgue Spaces ◽  
Carleson Curve

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 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 Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Qinghua Zhang ◽  
Yueping Zhu ◽  
Feng Wang
Keyword(s):  
Singular Integral ◽  
Evolution Equations ◽  
Maximal Regularity ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Sectorial Operators ◽  
Variable Lebesgue Spaces ◽  
Scalar Type ◽  
Semilinear Evolution Equations

This paper is devoted to the maximal regularity of sectorial operators in Lebesgue spaces Lp⋅ with a variable exponent. By extending the boundedness of singular integral operators in variable Lebesgue spaces from scalar type to abstract-valued type, the maximal Lp⋅−regularity of sectorial operators is established. This paper also investigates the trace of the maximal regularity space E01,p⋅I, together with the imbedding property of E01,p⋅I into the range-varying function space C−I,X1−1/p⋅,p⋅. Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into account.

scholarly journals Rough singular integrals on product spaces

2004 ◽  
Vol 2004 (67) ◽  
pp. 3671-3684 ◽  
Author(s):  
Ahmad Al-Salman ◽  
Hussain Al-Qassem
Keyword(s):  
Finite Type ◽  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Product Spaces ◽  
Lebesgue Spaces ◽  
Block Spaces ◽  
Singular Kernels

We study the mapping properties of singular integral operators defined by mappings of finite type. We prove that such singular integral operators are bounded on the Lebesgue spaces under the condition that the singular kernels are allowed to be in certain block spaces.

Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces

2020 ◽  
Vol 70 (4) ◽  
pp. 893-902
Author(s):  
Ismail Ekincioglu ◽  
Vagif S. Guliyev ◽  
Esra Kaya
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Bessel Differential Operator

AbstractIn this paper, we prove the boundedness of the Bn maximal operator and Bn singular integral operators associated with the Laplace-Bessel differential operator ΔBn on variable exponent Lebesgue spaces.

Boundedness of weighted singular integral operators in grand Lebesgue spaces

2011 ◽  
Vol 18 (2) ◽  
pp. 259-269
Author(s):  
Vakhtang Kokilashvili ◽  
Stefan Samko
Keyword(s):  
Singular Integral ◽  
Lebesgue Space ◽  
Sufficient Conditions ◽  
Singular Integral Equations ◽  
Lebesgue Spaces ◽  
Grand Lebesgue Spaces ◽  
Carleson Curve ◽  
Power Weights ◽  
Necessary And Sufficient ◽  
Grand Lebesgue Space

Abstract We obtain the necessary and sufficient conditions for the boundedness of the weighted singular integral operator with power weights in grand Lebesgue spaces. Because of applications to singular integral equations, the underlying set on which the functions are defined is a Carleson curve in the complex plane. Note that weighted boundedness of an operator in grand Lebesgue space is not the same as the boundedness in weighted grand Lebesgue space.

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