Multilinear Calderón-Zygmund Operators and Their Commutators with BMO Functions in Herz-Morrey Spaces with Variable Smoothness and Integrability

In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.

Boundedness for Commutators of Calder o′n-Zygmund Operator on Morrey Spaces with Variable Exponent

Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.

Commutator of Marcinkiewicz Integral Operators on Herz-Morrey-Hardy Spaces with Variable Exponents

In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [b,μΩ] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents .

Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.

Boundedness of Fractional Integral with Variable Kernel and Their Commutators on Variable Exponent Herz Spaces

In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents . By using the properties of the variable exponents Lebesgue spaces, the boundedness of the fractional integral operator and their commutator generated by Lipschitz function is obtained on those Herz spaces.

Boundedness for Commutators of Calderón-Zygmund Operator on Herz-Type Hardy Space with Variable Exponent

Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.

Multilinear Calderon-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces

The boundedness of multilinear Calderdn-Zygmund operators and their commutators with bounded mean oscillation （BMO） functions in variable exponent Morrey spaces are obtained.

Commutators of Littlewood-Paley Operators on Herz Spaces with Variable Exponent

Let Ω ∈ L^2（S^n-1） be homogeneous function of degree zero and b be BMO functions. In this paper, we obtain some boundedness of the Littlewood-Paley Opera- tors and their higher-order commutators on Herz spaces with variable exponent.

Vector-valued Inequalities for Commutators of Singular Integrals on Herz Spaces with Variable Exponents

Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents.Furthermore, we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.

Boundedness of Calderón-Zygmund Operator and Their Commutator on Herz Spaces with Variable Exponent

The aim of this paper is to study the boundedness of Calderón-Zygmund operator and their commutator on Herz Spaces with two variable exponents p(.),q(.). By applying the properties of the Lebesgue spaces with variable exponent, the boundedness of the Calderón-Zygmund operator and the commutator generated by BMO function and Calderón-Zygmund operator is obtained on Herz space.

λ-central BMO Estimates for Higher Order Commutators of Hardy Operators

In this paper, the λ-central BMO estimates for higher order commuta-tors of Hardy operators on central Morrey space Lq,λ（Rn） are established. In the meanwhile, the corresponding corollary for central BMO estimates is also obtained.

Multilinear singular integrals and commutators in variable exponent Lebesgue spaces

Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.

CBMO Estimates for Commutators of Fractional Integral Operators with Variable Kernels

In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.

Characterizations of the BMO and Lipschitz Spaces via Commutators on Weak Lebesgue and Morrey Spaces

We prove that the weak Morrey space W M_(q)^(p) is contained in the Morrey space M_(q1)^(p) for 1 ≤ q1<q ≤ p < ∞. As applications, we show that if the commutator [b, T ] is bounded from L^(p) to L^(p,∞) for some p ∈(1, ∞), then b ∈ BMO, where T is a Calderón-Zygmund operator. Also, for 1 < p ≤ q < ∞, b ∈ BMO if and only if [b, T ] is bounded from M_(q)^(p) to WM_(q)^(p). For b belonging to Lipschitz class, we obtain similar results.

Boundedness for Commutators of Approximate Identities on Weighted Morrey Spaces

The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces

The Boundedness of Multilinear Commutators on Grand Variable Herz Spaces

We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is a family of m locally integrable functions.Based on the theory of variable exponent and on generalization of the BMO norm,we prove the boundedness of multilinear commutators T_(b) on grand variable Herz spaces.The result is still new even in the special case of m=1.

Bilinear Pseudo-Differential Operator and Its Commutator on Generalized FractionalWeighted Morrey Spaces

The aim of this paper is to establish the boundedness of bilinear pseudodifferential operator Ts and its commutator[b1,b2,Ts]generated by Ts and b1,b22 BMO(Rn)on generalized fractional weighted Morrey spaces Lp,h,j(w).Under assumption that a weight satisfies a certain condition,the authors prove that Ts is bounded from products of spaces Lp1,h1,j(w1)Lp2,h2,j(w2)into spaces Lp,h,j(~w),where~w=(w1,w2)2 A~P,~P=(p1,p2),h=h1+h2 and 1 p=1 p1+1 p2 with p1,p22(1,¥).Furthermore,the authors show that the[b1,b2,Ts]is bounded from products of generalized fractional Morrey spaces Lp1,h1,j(Rn)Lp2,h2,j(Rn)into Lp,h,j(Rn).As corollaries,the boundedness of the Ts and[b1,b2,Ts]on generalized weighted Morrey spaces Lp,j(w)and on generalized Morrey spaces Lp,j(Rn)is also obtained.

Weighted Estimates of Variable Kernel Fractional Integral and Its Commutators on Vanishing Generalized Morrey Spaces with Variable Exponent

In this paper,the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized weighted Morrey spaces.And the corresponding commutators generated by BMO function are also considered.

Commutators of Bilinear Hardy Operators on Two Weighted Herz Spaces with Variable Exponents

In this paper,we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of two weighted Herz spaces.

Boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents

We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its commutator.