Morrey-Herz Spaces Research Articles

Weighted Morrey–Herz space estimates for rough Hausdorff operator and its commutators

In this paper, we give necessary and sufficient conditions for the boundedness of rough Hausdorff operators on Herz, Morrey and Morrey–Herz spaces with absolutely homogeneous weights. Especially, the estimates for operator norms in each case are worked out. Moreover, we also establish the boundedness of the commutators of rough Hausdorff operators on the two weighted Morrey–Herz type spaces with their symbols belonging to Lipschitz space. By these, we obtain some new estimates for the high dimensional Hardy operator and adjoint Hardy operator.

Some Estimates for p-Adic Rough Multilinear Hausdorff Operators and Commutators on Weighted Morrey–Herz Type Spaces

The aim of this paper is to introduce and study the boundedness of a new class of p-adic rough multilinear Hausdorff operators on the product of Herz, central Morrey and Morrey-Herz spaces with power weights and Muckenhoupt weights. We also establish the boundedness for the commutators of p-adic rough multilinear Hausdorff operators on the weighted spaces with symbols in central BMO space.

Higher order commutators of fractional integrals on Morrey type spaces with variable exponents

AbstractBased on the theory of variable exponent and BMO norms, we prove some boundedness results for the m‐th order commutators of the fractional integrals on variable exponent Morrey and Morrey–Herz spaces. Even in the special case of , the main results obtained are also new.

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Let T be the singular integral operator with variable kernel defined by Tf(x)=p.v.∫Rn(Ω(x,x-y)/x-yn)f(y)dy and let Dγ (0≤γ≤1) be the fractional differentiation operator. Let T⁎and T♯ be the adjoint of T and the pseudoadjoint of T, respectively. In this paper, the authors prove that TDγ-DγT and (T⁎-T♯)Dγ are bounded, respectively, from Morrey-Herz spaces MK˙p,1α,λ(Rn) to the weak Morrey-Herz spaces WMK˙p,1α,λ(Rn) by using the spherical harmonic decomposition. Furthermore, several norm inequalities for the product T1T2 and the pseudoproduct T1∘T2 are also given.

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.

Some estimates of Hardy operators and their commutators on Morrey-Herz spaces

Some estimates of Hardy operators and their commutators on Morrey-Herz spaces

Bounds for the Weighted Hardy-Cesàro Operator and its Commutator on Morrey-Herz Type Spaces

In this paper we will prove the boundedness of weighted Hardy-Cesàro operator on Herz and Morrey-Herz spaces with absolutely homogeneous weights. The corresponding operator norms are obtained. We also prove the boundedness of the commutators of Hardy-Cesàro operator on weighted spaces of Morrey-Herz type, with their symbols belong to Lipschitz space. By these we extend and strengthen previous results due to Kuang [15], Fu et al. [9] and Tang et al. [20].

Boundedness of rough singular integral operators and commutators on Morrey-Herz spaces with variable exponents

By decomposing functions, we establish some boundedness results for some rough singular integrals on the homogeneous Morrey-Herz spaces $M\dot{K}_{q, p(\cdot)}^{\alpha(\cdot),\lambda}({\Bbb{ R}}^{n})$ , where the two main indices are variable. The corresponding results as regards their commutators are also considered.

The p-adic weighted Hardy-Cesàro operators on weighted Morrey-Herz space

In this article we give necessary and sufficient conditions for the boundedness of the weighted Hardy-Cesa ro operators which is associated to the parameter curve γ(t, x) = γ(t)x defined by \({U_{\psi ,\gamma }}f\left( x \right) = \int {\left( {\gamma \left( t \right)x} \right)} \psi \left( t \right)dt\) on the weighted Morrey-Herz space over the p-adic field. Especially, the corresponding operator norms are established in each case. These results actually extend those of K. S. Rim and J. Lee [27] and of the authors [9]. Moreover, the sufficient conditions of boundedness of commutators of p-adic weighted Hardy-Cesaro operator with symbols in the Lipschitz space on the weighted Morrey-Herz space are also established.

Some estimates for commutators of Hausdorff operators

In this paper, we establish some new estimates for commutators of Hausdorff operators on homogeneous Herz and Morrey-Herz spaces, which extend some previous results.

WEIGHTED LIPSCHITZ ESTIMATES FOR COMMUTATORS ON WEIGHTED MORREY-HERZ SPACES

In this paper, the authors establish the boundedness of commutators generated by Calder o n-Zygmund singular integral operators and weighted Lipschitz functions on weighted Morrey-Herz spaces.

WEIGHTED LIPSCHITZ ESTIMATES FOR COMMUTATORS ON WEIGHTED MORREY-HERZ SPACES

In this paper, the authors establish the boundedness of commutators generated by Calder o n-Zygmund singular integral operators and weighted Lipschitz functions on weighted Morrey-Herz spaces.

Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

We introduce a new type of variable exponent function spaces \(M\dot K_{q,p( \cdot )}^{\alpha ( \cdot ),\lambda } (\mathbb{R}^n )\) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderon-Zygmund operators and their commutators of BMO function on these Morrey-Herz type spaces by applying the properties of variable exponent and BMO norms.

Boundedness of the Commutators of Fractional Maximal Operator on Morrey-Herz Space on Spaces of Homogeneous Type

In this paper,with the help of the boundedness of the commutators of the fractional Hardy-Littlewood maximal operator on L~p(X),the boundedness of the commutators of the fractional Hardy-Littlewood maximal operator on Morrey-Herz space on spaces of homogeneous type is proved.

Weighted Multilinear Hardy Operators on Herz Type Spaces

This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained results to the product Morrey-Herz spaces.

Multidimensional Hausdorff operators and commutators on Herz-type spaces

In this paper, we give necessary and sufficient conditions for the boundedness of the n-dimensional Hausdorff operators on Herz-type spaces. In addition, the sufficient condition for the boundedness of commutators generated by Lipschitz functions and the fractional Hausdorff operators on Morrey-Herz space is also provided. MSC:26D15, 42B35, 42B99.

The boundedness of sublinear operators on Morrey-Herz spaces over the homogeneous type space

In this article, the Morrey-Herz spaces over the homogeneous type basic space are introduced; moreover, several theorems about the boundedness of some sublinear operators on these Morrey-Herz spaces are established, which extend the related known results.

Boundedness of Multilinear Commutators with Rough Kernels on Morrey-Herz Spaces

This paper is concerning the commutators generated by the multilinear singular integral with rough kernels and BMO functions. The boundedness of the multilinear commutators Tb(f) is established on the Morrey-Herz space by using the JohnNirenberg inequality.

Boundedness for Multilinear Commutators of Marcinkiewicz Integral on Morrey-Herz Spaces with Non Doubling Measures

In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO(μ) function on homogeneous Morrey-Herz spaces with non doubling measures.

Weighted Hardy-Littlewood operators and commutators on p-adic functional spaces

In this paper we give necessary and sufficient conditions for the boundedness of the weighted Hardy-Littlewood averages and the weighted Cesaro averages on p-adic Triebel-Lizorkin spaces and p-adic Morrey-Herz spaces. Especially, the corresponding operator norms in each case are established. Furthermore, sufficient conditions of the boundedness of the commutators of weighted Hardy-Littlewood operators, and weighted Cesaro operators with symbols in the Lipschitz spaces on p-adic Morrey-Herz spaces are also given.