Herz-type Hardy Spaces Research Articles

Weak Type Estimate of Singular Integral Operators on Variable Weak Herz-Type Hardy Spaces

This paper is concerned with the boundedness properties of singular integral operators on variable weak Herz spaces and variable weak Herz-type Hardy spaces. Allowing our parameters to vary from point to point will raise extra difficulties, which, in general, are overcome by imposing regularity assumptions on these exponents, either at the origin or at infinity. Our results cover the classical results on weak Herz-type Hardy spaces with fixed exponents.

Weighted Grand Herz-Type Spaces and Its Applications

In this paper, we introduce the weighted grand Herz spaces and weighted grand Herz-type Hardy spaces. The decompositional characterizations of these spaces are established. As its applications, the boundedness of some sublinear operators are established.

Herz-type Hardy spaces with variable exponents associated with operators satisfying Davies–Gaffney estimates

Herz-type Hardy spaces with variable exponents associated with operators satisfying Davies–Gaffney estimates

Endpoint estimates for multilinear fractional singular integral operators on Herz and Herz type Hardy spaces

<abstract> The boundedness of singular and fractional integral operator on Lebesgue and Hardy spaces have been well studied. The theory of Herz space and Herz type Hardy space, as a local version of Lebesgue and Hardy space, have been developed. The main purpose of this paper is to establish the endpoint continuity properties of some multilinear operators related to certain non-convolution type fractional singular integral operators on Herz and Herz type Hardy spaces and the endpoint estimates for the multilinear operators on Herz and Herz type Hardy spaces are obtained. </abstract>

Some Characterization of Herz and Herz-Type Hardy Spaces for the Dunkl Operator

In this work, new characterizations of Herz and Herz-type Hardy spaces associated with the Dunkl operator on the real line are introduced.

Weak type estimates of commutators on Herz type spaces with variable exponent

In this paper, first we establish the weak type estimates of the commutators of the maximal operator, the fractional maximal operator and some commutators related to linear operators on the Herz type spaces with variable exponent. Subsequently the weak type Lipschitz estimates of Calderón–Zygmund singular integral commutator and fractional integral commutator from Herz-type Hardy spaces with variable exponent to weak Herz spaces with variable exponent are obtained.

Variable Herz estimates for fractional integral operators

UDC 517.5 In this paper, the author study the boundedness of fractional integral operators on a variable Herz-type Hardy space by using the atomic decomposition.

The molecular characterization of anisotropic Herz-type Hardy spaces with two variable exponents

Abstract In this article, the authors establish the characterizations of a class of anisotropic Herz-type Hardy spaces with two variable exponents associated with a non-isotropic dilation on ℝ n {{\mathbb{R}}}^{n} in terms of molecular decompositions. Using the molecular decompositions, the authors obtain the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy space with two variable exponents.

Boundedness of singular integral operators on weak Herz type spaces with variable exponent

In this paper, the authors define the weak Herz spaces and the weak Herz-type Hardy spaces with variable exponent. As applications, the authors establish the boundedness for a class of singular integral operators including some critical cases.

Parametrized Littlewood–Paley Operators on Herz-Type Hardy Spaces with Variable Exponent

In this paper, the authors establish the boundedness of parametrized Littlewood–Paley area integral and $$g^*_\lambda $$ -function, and their high-order commutators on Herz-type Hardy spaces with variable exponent. These results are also new even for classical Herz-type Hardy space.

Strongly Singular Convolution Operators on Herz-Type Hardy Spaces with Variable Exponent

We investigate the boundedness of the strongly singular convolution operators on Herz-type Hardy spaces with variable exponent.

Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces

In this paper, we prove the boundedness of matrix Hausdorff operators and rough Hausdorff operators in the two weighted Herz-type Hardy spaces associated with both power weights and Muckenhoupt weights. By applying the fact that the standard infinite atomic decomposition norm on two weighted Herz-type Hardy spaces is equivalent to the finite atomic norm on some dense subspaces of them, we generalize some previous known results due to Chen et al. [7] and Ruan, Fan [35].

On n-dimensional fractional Hardy operators and commutators in variable Herz-type spaces

Based on the theory of variable exponents and atomic decomposition, we study the boundedness of n-dimensional fractional Hardy operators on variable Herz and Herz-type Hardy spaces, where the three main indices are variable exponents. The corresponding boundedness for the mth order commutators generated by the n-dimensional fractional Hardy operators and bounded mean oscillation (BMO) function are also considered. We note that, even in the special case of m=1, the obtained results are also new.

Herz type Hardy spaces on non-homogeneous metric measure space

Let $(\mathcal{X},d,\mu)$ be a non-homogeneous metric measure spacesatisfying both the geometrically doubling and the upper doublingconditions. In this paper, the Herz spaces on the non-homogeneousmetric measure space are introduced. Then the decomposition of theHerz space by the central blocks is obtained. The atomic Herz typeHardy spaces and the molecular Herz type Hardy spaces on thenon-homogeneous metric measure space via the discrete coefficient${\widetilde~K}_{B,S}^{(\rho),p}$ are also defined. In addition, theequivalence of the atomic Herz type Hardy spaces and the molecularHerz type Hardy spaces is established. As the applicationsof these spaces, some boundedness of Calderon-Zygmund operatorson the Herz type Hardy spaces are discussed.

Herz-Type Hardy Spaces Associated with Operators

Suppose L is a nonnegative, self-adjoint differential operator. In this paper, we introduce the Herz-type Hardy spaces associated with operator L. Then, similar to the atomic and molecular decompositions of classical Herz-type Hardy spaces and the Hardy space associated with operators, we prove the atomic and molecular decompositions of the Herz-type Hardy spaces associated with operator L. As applications, the boundedness of some singular integral operators on Herz-type Hardy spaces associated with operators is obtained.

Anisotropic Herz-type Hardy spaces with variable exponent and their applications

A class of anisotropic Herz-type Hardy spaces with variable exponent associated with a non-isotropic dilation on $${\mathbb{R}^{n}}$$ are introduced, and characterizations of these spaces are established in terms of atomic and molecular decompositions. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of a linear operator on the anisotropic Herz-type Hardy spaces with variable exponent.

Weighted Hardy Type Spaces Estimates of Multilinear Singular Integral Operators for the Extreme Cases

We prove the weighted endpoint estimates for some multilinear operators related to certain singular integral operators on some Hardy and Herz type Hardy spaces.

Multilinear Commutators of Singular Integral Operators in Variable Exponent Herz-Type Spaces

In this paper, we study the boundedness of multilinear commutators of Hardy–Littlewood maximal operators in variable exponent Herz and Herz–Morrey spaces, which in turn are used to obtain the boundedness for a large class of the multilinear commutators related to sublinear operators. Moreover, based on the atomic decomposition and on generalization of the BMO norm, we study the boundedness of multilinear commutators of singular integral operators with Calderon–Zygmund kernels in variable exponent Herz-type Hardy spaces.

Central Calderón–Zygmund operators on Herz-type Hardy spaces of variable smoothness and integrability

In this article we use the atomic decomposition of a Herz-type Hardy space of variable smoothness and integrability to obtain the boundedness of the central Calderon–Zygmund operators on Herz-type Hardy spaces with variable smoothness and integrability.

Commutators of homogeneous fractional integrals on Herz-type Hardy spaces with variable exponent

Let Ω ∈ L s (S n−1), s ≥ 1, be a homogeneous function of degree zero, and let σ (0 < σ < n) and b be Lipschitz or BMO functions. In this paper, we establish the boundedness of the commutators [b, T Ω,σ ], generated by a homogeneous fractional integral operator T Ω,σ and function b, on the Herz-type Hardy spaces with variable exponent.