Some estimates for the commutators of multilinear maximal function on Morrey-type space

In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

The aim of this paper is to deal with the boundedness of the θ-type Calderón-Zygmund operators and their commutators on Herz spaces with two variable exponents p(⋅), q(⋅). It is proved that the θ-type Calderón-Zygmund operators are bounded on the homogeneous Herz space with variable exponents $\begin{array}{} \displaystyle \dot{K}^{\alpha,q(\cdot)}_{p(\cdot)}(\mathbb{R}^{n}). \end{array}$ Furthermore, the boundedness of the corresponding commutators generated by BMO function and Lipschitz function is also obtained respectively.

Precompact Sets, Boundedness, and Compactness of Commutators for Singular Integrals in Variable Morrey Spaces

We give sufficient conditions for subsets to be precompact sets in variable Morrey spaces. Then we obtain the boundedness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces. Finally, we discuss the compactness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces.

Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels

We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator TΩ,σ and its commutator [b,TΩ,σ] on Morrey-Herz space with variable exponent, where Ω∈Ls(Sn-1) for s≥1 is a homogeneous function of degree zero, 0<σ<n, and b is a BMO function.

Relation Between BMO and A2 Weight Functions

In this paper, we relate Bounded Mean Oscillation (BMO) function and A2 weight function. We show that logarithm of any A2 function is a BMO function and every BMO function is equal to a constant multiple of the logarithm of an A2 weight function. Moreover, we show that logarithm of any Ap weight function for 1 < p < ∞ is a BMO function.

Weighted BMO Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operator

Schrödinger operator; Weighted BMO spaces; Reverse Hölder inequality; Commutator Abstract. In this paper, the Schrödinger operator on n dimensions Euclid space with the non-zero, nonnegative potential function satisfying the reverse Hölder inequality is considered. The weighted boundedness of the commutators composed of several Riesz transforms associated with the Schrödinger operator and weighted BMO function on weighted Lebesgue integral spaces are obtained, for some weighted function.

New Weighted Norm Inequalities for Pseudodifferential Operators and Their Commutators

This paper is dedicated to study weighted inequalities for pseudodifferential operators with amplitudes and their commutators by using the new class of weights and the new BMO function space BMO∞ which are larger than the Muckenhoupt class of weights and classical BMO space BMO, respectively. The obtained results therefore improve substantially some well-known results.

Existence and Boundedness of Parametrized Marcinkiewicz Integral with Rough Kernel on Campanato Spaces

Let g(f), S(f), g*λ(f) be the Littlewood-Paley g function, Lusin area function, and Littlewood-Paley g*λ(f) function of f, respectively. In 1990 Chen Jiecheng and Wang Silei showed that if, for a BMO function f, one of the above functions is finite for a single point in ℝn, then it is finite a.e. on ℝn, and BMO boundedness holds. Recently, Sun Yongzhong extended this result to the case of Campanato spaces (i.e. Morrey spaces, BMO, and Lipschitz spaces). One of us improved his g*λ(f) result further, and treated parametrized Marcinkiewicz functions with Lipschitz kernel μρ(f), μρs(f) and μλ*,ρ(f). In this paper, we show that the same results hold also in the case of rough kernel satisfying Lp-Dini type condition.

The higher order commutators of the fractional integrals on Hardy spaces

In this paper we investigate the boundedness on Hardy spaces for the higher order commutator Tb, m generated by the BMO function b and fractional integral type operator Tτ, and establish the boundness theorems for Tτb, m from Hp1.q1.sb, m to Lp2 and to Hp2 (0 < p1 ≤ 1), and from H Ka. p1.sq1, b, m to Ka.p2q2 and to H Ka. p2q2, respectively, for certain ranges of α, p1, q1, p2, q2 and s.

Hardy spaces estimates for multilinear operators with homogeneous kernels

In this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spaces Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.