Herz Spaces Research Articles

Publisher Correction: Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index

Publisher Correction: Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index

Hardy–Littlewood maximal function on Lorentz–Herz spaces

AbstractThis paper extends the study of the generalized Lorentz spaces to the Lorentz–Herz spaces. The Lorentz–Herz spaces consist of all Lebesgue measurable functions such that theirs non-increasing rearrangements belong to the weighted Herz space. The main result of this paper establishes the mapping properties of the Hardy–Littlewood maximal function on the Lorentz–Herz spaces.

Trace principle for Riesz potentials on Herz-type spaces and applications

We establish trace inequalities for Riesz potentials on Herz-type spaces and examine the optimality of conditions imposed on specific parameters. We also present some applications in the form of Sobolev-type inequalities, including the Gagliardo–Nirenberg–Sobolev inequality and the fractional integration theorem in the Herz space setting. In addition, we obtain a Sobolev embedding theorem for Herz-type Sobolev spaces.

Localized operators on weighted Herz spaces

AbstractWe introduce the notion of localized operators. We extend the boundedness of the localized operators from the weighted Lebesgue spaces to the weighted Herz spaces. The localized operators include the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function. Therefore, this paper extends the mapping properties of the the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function to the weighted Herz spaces.

Generalized Product Hausdorff Operator on Two-Weighted Morrey–Herz Spaces

Generalized Product Hausdorff Operator on Two-Weighted Morrey–Herz Spaces

Mixed radial-angular integrabilities for commutators of fractional Hardy operators

In this paper, we introduce the mixed radial-angular homogeneous CMO spaces CMOLradp2Langp1(Rn) and the mixed radial-angular Herz spaces K˙Lradp2Langp1α,q(Rn), respectively. Furthermore, the boundedness of commutators Hβ,b generated by the fractional Hardy operators Hβ with a function b in CMOLradp2Langp1(Rn) are established on K˙Lradp2Langp1α,q(Rn). Meanwhile, the corresponding results for Hβ,b when b∈CMOLradp2,λLangp1(Rn), the mixed radial-angular homogeneous λ-central bounded mean oscillation spaces, are also considered on BLradp2,λLangp1(Rn), the mixed radial-angular homogeneous λ-central Morrey spaces.

Estimates for Hausdorff operator associated with the Opdam–Cherednik transform and its commutator on weighted Morrey–Herz spaces

Estimates for Hausdorff operator associated with the Opdam–Cherednik transform and its commutator on weighted Morrey–Herz spaces

Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces

Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces

Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index

Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index

Extrapolation to two-weighted Herz spaces with three variable exponents

Extrapolation to two-weighted Herz spaces with three variable exponents

Commutators of bilinear $$\theta $$-type Calderón–Zygmund operators on two weighted Herz spaces with variable exponents

Commutators of bilinear $$\theta $$-type Calderón–Zygmund operators on two weighted Herz spaces with variable exponents

Extrapolation to mixed Herz spaces and its applications

AbstractIn this paper, we extend the extrapolation theory to mixed Herz spaces and . To prove the main result, we first study the dual spaces of mixed Herz spaces, and then give the boundedness of the Hardy–Littlewood maximal operator on mixed Herz spaces. By using the extrapolation theorems, we obtain the boundedness of many integral operators on mixed Herz spaces. We also give a new characterization of via the boundedness of commutators of some operators on mixed Herz spaces.

Boundedness for Commutators of Singular Integral Operator With Weaker Smooth Kernel on Weighted Hardy and Herz Spaces

In this job, let T be a variant of Hörmander’s singular operator and b ∈ Lipβ,ω(ℝn). We adopt the classic Harmonic analysis method and obtain that commutators are bounded on weighted Hardy space and weighted Herz space.

On the well-posedness in Besov–Herz spaces for the inhomogeneous incompressible Euler equations

On the well-posedness in Besov–Herz spaces for the inhomogeneous incompressible Euler equations

Hardy–Littlewood maximal operators and Hausdorff operators on $ p $-adic block spaces with variable exponents

<p>In this paper, we established some sufficient conditions for the boundedness of the Hardy–Littlewood maximal operators and the Hausdorff operators on $ p $-adic Herz spaces and $ p $-adic local block spaces with variable exponents. In particular, the boundedness of the $ p $-adic maximal commutator operators, the $ p $-adic Hardy–Littlewood average operators, and the $ p $-adic Hardy-Hilbert operators on such spaces was also discussed.</p>

Rough Fractional Hausdorff Operators on Morrey–Herz Spaces with Variable Exponents

Rough Fractional Hausdorff Operators on Morrey–Herz Spaces with Variable Exponents

Boundedness Analysis of the Fractional Maximal Operator in Grand Herz Space on the Hyperplane

The primary purpose of this work was to prove the boundedness of the Fractional Maximal Operator in Grand Herz Spaces on the Hyperplane. Here, We defined Grand Herz Space in a continuous Case. For Simplicity, We divided our Problem into two theorems by taking two subsets of Hyperplane( ) as ( ) and its complement . We proved the boundedness of the Fractional Maximal Operator in Grand Herz Space on these two subsets of Hyperplane. We also defined the continuous Case of Grand Herz Space. We proved some results to use in our proof. We represented other terms this paper uses, i.e. the Hyperplane and Fractional Maximal operator. Our proof method relied on one of the corollaries we gave in this paper. We proved the condition to apply that corollary, and then by referring to this, we confirmed both of our theorems. This paper is helpful in Harmonic analysis and delivers ways to analyse the solutions of partial differential equations. The Problem of our discussion provides methods to study the properties of very complex functions obtained from different problems from Physics, Engineering and other branches of science. Solutions of nonlinear Partial Differential equations often resulted in such functions which required deep analysis. Our work helps check the boundedness of such types of functions.

Boundedness of commutators of rough Hardy operators on grand variable Herz spaces

Abstract The aim of this paper is to obtain the boundedness of commutators of Hardy operators with rough kernels on grand variable Herz spaces K ˙ q ⁢ ( ⋅ ) a ⁢ ( ⋅ ) , u , θ ⁢ ( ℝ n ) {\dot{K}^{a(\,\cdot\,),u,\theta}_{q(\,\cdot\,)}(\mathbb{R}^{n})} by applying some properties of variable exponent. Moreover, by using the idea of grand variable Herz–Morrey spaces, we will prove the boundedness of Hardy operators on these spaces.

Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces

Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces

Two Weighted Norm Inequalities of Potential Type Operator on Herz Spaces

Two Weighted Norm Inequalities of Potential Type Operator on Herz Spaces