Variable <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>λ</mi> </math>-Central Morrey Space Estimates for the Fractional Hardy Operators and Commutators

Commutators of Littlewood-Paley Operators on the Generalized Morrey Space

Weighted Estimates for Bilinear Fractional Integral Operators and Their Commutators

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 esti...

Hardy Space Estimates for Multilinear Operators, Ii

We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue spaces Lp(Rn) into the Hardy spaces Hr(Rn). At the endpoint case r = n/n+m+ 1, where m is the highest vanishing moment of the multilinear operator, we prove a weak type result. 0. Introduction A wel...

Commutators of integral operators with variable kernels on Hardy spaces

Abstract. Let TΩ,α (0 ≤ α < n) be the singular and fractional integrals with variable kernel Ω(x,z), and [b,TΩ,α ] be the commutator generated by TΩ,α and a Lipschitz function b. In this paper, the authors study the boundedness of [b,TΩ,α ] on the Hardy spaces, under some assumptions such as the Lr-Dini condition. Similar results and the weak type estimates at the end-point cases are also given...

Weighted 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...