Singular Integral Operators with Fixed Singularities on Weighted Lebesgue Spaces

2004 ◽  
Vol 48 (3) ◽  
pp. 331-363 ◽  
Author(s):  
Yu. I. Karlovich ◽  
E. Ram�rez de Arellano
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

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 Lipschitz Estimates for One-Sided Cohen’s Commutators on Weighted One-Sided Triebel-Lizorkin Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiao Jin Zhang ◽  
Xian Ming Hou
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Weighted Lebesgue Spaces ◽  
Lipschitz Estimates

We introduce one-sided Cohen’s commutators of singular integral operators and fractional integral operators, respectively. Using the extrapolation of one-sided weights, we establish the boundedness of these operators from weighted Lebesgue spaces to weighted one-sided Triebel-Lizorkin spaces.

scholarly journals Multilinear strongly singular integral operators with generalized kernels and applications

2021 ◽  
Vol 6 (12) ◽  
pp. 13533-13551
Author(s):  
Shuhui Yang ◽  
◽  
Yan Lin
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces

<abstract><p>In this paper, the authors study the boundedness properties of a class of multilinear strongly singular integral operator with generalized kernels on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces, respectively. Moreover, the types $ L^{\infty}\times \dots \times L^{\infty}\rightarrow BMO $ and $ BMO\times \dots \times BMO\rightarrow BMO $ endpoint estimates are also obtained.</p></abstract>

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 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.

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