Weighted Estimates for Bilinear Fractional Integral Operators and Their Commutators
نویسندگان
چکیده
In this paper we will prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted Lp norm is bounded by the weighted Lp norm of a natural maximal operator when the weight belongs to A∞. As a corollary we are able to obtain new weighted estimates for the bilinear maximal function associated to the bilinear Hilbert transform. Finally, as an application of our results we prove a bilinear Stein-Weiss inequality.
منابع مشابه
Compactness Properties of Commutators of Bilinear Fractional Integrals
Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional integral versions of the bilinear Hilbert transform yield separately compact operators.
متن کاملLipschitz Estimates for Multilinear Commutator of Pseudo-differential Operators
As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [4, 5, 6, 7, 8, 9, 10]). In [4, 5, 6, 7, 8, 9, 10], the authors prove that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on L(R) for 1 < p <∞; Chanillo (see [2]) proves a similar result when singular int...
متن کاملWeighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces
In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators [Formula: see text] in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutator...
متن کاملAdams-spanne Type Estimates for Certain Sublinear Operators and Their Commutators Generated by Fractional Integrals in Generalized Morrey Spaces on Heisenberg Groups and Some Applications
In this paper we consider the Spanne type boundedness of sublinear operators and prove the Adams type boundedness theorems for these operators and also give BMO (bounded mean oscillation space) estimates for their commutators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are formulated in terms of Zygmund type integral inequalities. Based on the properties of the...
متن کاملLipschitz Estimates for Commutators of Singular Integral Operators on Weighted Herz Spaces
In this paper, we establish the boundedness of commutators generated by weighted Lipschitz functions and Calderón-Zygmund singular integral operators on weighted Herz spaces.
متن کامل