Sharp Maximal Function Estimates and Boundedness for Commutator Related to Generalized Fractional Integral Operator
TL;DR: In this paper, the maximal function estimates for the commutators related to a generalized fractional integral operator with general kernel and the BMO and Lipschitz functions were obtained. But the maximal functions were not obtained for all commutator functions.
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Abstract: In this paper, we prove some sharp maximal function estimates for the commutators related to certain generalized fractional integral operator with general kernel and the BMO and Lipschitz functions. As an application, we obtain the boundedness of the commutators on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operator includes fractional Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.
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Citations
•Journal Article
Endpoint Estimate for Commutators of Singular Integral Operators on Hrmander Condition
TL;DR: In this article, the authors discuss the end-piont estimate for the commutator whose kernel satisfies the Hormander condition, i.e., it is bounded from to BMO.
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Interior estimates in morrey spaces for solutions of elliptic equations and weighted boundedness for commutators of singular integral operators
刘岚喆
- 01 Jan 2005
TL;DR: In this paper, it was proved that the commutators of some singular integral operators on Lp,ψ (ω) are weighted bounded by the W2,p-solution of the equations.
34
References
•Book
Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals
Elias M. Stein,Timothy S Murphy +1 more
- 01 Jan 2002
TL;DR: In this article, the authors introduce the Heisenberg group and describe the Maximal Operators and Maximal Averages and Oscillatory Integral Integrals of the First and Second Kind.
7.7K
•Book
Weighted norm inequalities and related topics
José García-Cuerva,J.-L. Rubio de Francia +1 more
- 01 Jan 1985
TL;DR: Theories de la factorisation and inegalites en norme ponderees of Hardy as mentioned in this paper have been studied in the context of factorization, and a variable reelle des espaces de Hardy has been proposed.
2.2K
Factorization theorems for Hardy spaces in several variables
TL;DR: In this article, the authors extend the duality between HI and BMO in terms of boundedness on L 2 of the commutator of a singular integral operator with a multiplication operator and show a close relationship between BMO functions and certain linear operators on various LI and H2 spaces.
1.5K
Weighted norm inequalities for fractional integrals
TL;DR: The main result of as discussed by the authors is that V(x) is such a function if and only if (-fQ [V(X)]qdx (jff [vx) P'd)1 (IQIJQVX]^ (QI J [V[V[X)]-p, ) where Q is any n dimensional cube, IQI denotes the measure of Q, p' = p/(p 1) and K is a constant independent of Q. Substitute results for the cases p = 1 and q = oo and a weighted version
On the theory of Lp,λ spaces
TL;DR: The theory of Lp,λ spaces as mentioned in this paper is a generalization of the theory of a priori estimates in the Lp norm, i.e., estimates in Lipα norm.
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