Herz-Morrey Spaces Research Articles

Homogeneous Grand Mixed Herz–Morrey Spaces and Their Applications

In this paper, we introduce the homogeneous grand mixed Herz–Morrey spaces MK˙q˜,λα,p),θ(Rn) and investigate their fundamental properties. We further explore the boundedness of sublinear operators and fractional-type operators on these spaces, establishing new results that contribute to the broader understanding of their applications.

Generalized Hölder Inequality in Herz-Morrey Spaces with Variable Exponent

The paper investigates the conditions for the generalized Hölder’s inequality with a variable exponent in Herz-Morrey spaces. The main results are based on the exponent functions p(·) and α(·) . The proof of the first main result using the generalized Hölder’s inequality in Lebesgue spaces. The second main result of the paper is related to the weak space of the generalized Hölder’s inequality with a variable exponent in Herz-Morrey spaces. The theorems state the equivalence of certain conditions for the inequality. Mathematical proofs and analysis are providing to support the presented results for findings contribute to the understanding of Hölder’s inequalities in variable exponent spaces and their applications in Herz-Morrey spaces.

Fractional type Marcinkiewicz integral and its commutator on grand variable Herz-Morrey spaces

Fractional type Marcinkiewicz integral and its commutator on grand variable Herz-Morrey spaces

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.

Boundedness of sublinear operators on weighted grand Herz-Morrey spaces

<abstract><p>In this paper, we introduce weighted grand Herz-Morrey type spaces and prove the boundedness of sublinear operators and their multilinear commutators on these spaces. The results are still new even in the unweighted setting.</p></abstract>

Boundedness of Fractional Integrals on Grand Weighted Herz–Morrey Spaces with Variable Exponent

In this paper, we introduce grand weighted Herz–Morrey spaces with a variable exponent and prove the boundedness of fractional integrals on these spaces.

Boundedness of Riesz Potential Operator on Grand Herz-Morrey Spaces

In this paper, we introduce grand Herz–Morrey spaces with variable exponent and prove the boundedness of Riesz potential operators in these spaces.

Inclusion Properties of The Homogeneous Herz-Morrey Spaces With Variable Exponent

In this paper, we have discussed about the inclusion properties of the homogeneous Herz-Morrey spaces with variable exponent and the weak homogeneous spaces with variable exponent. We also studied the inclusion relation between those spaces.

Commutators of the Fractional Hardy Operator on Weighted Variable Herz-Morrey Spaces

In the present paper, our aim is to establish the boundedness of commutators of the fractional Hardy operator and its adjoint operator on weighted Herz-Morrey spaces with variable exponents M K ̇ p , q ⋅ α ⋅ , λ w .

Commutators of Multilinear Calderón-Zygmund Operator on Weighted Herz-Morrey Spaces with Variable Exponents

In this paper, we acquire the boundedness of commutators generated by multilinear Calderón-Zygmund operator and BMO functions on products of weighted Herz-Morrey spaces with variable exponents.

Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents

Abstract If vector-valued sublinear operators satisfy the size condition and the vector-valued inequality on weighted Lebesgue spaces with variable exponent, then we obtain their boundedness on weighted Herz-Morrey spaces with variable exponents.

Hardy–Sobolev inequality for Sobolev functions in central Herz–Morrey spaces

AbstractOur aim in this paper is to establish Hardy–Sobolev inequality for Sobolev functions in central Herz–Morrey spaces. As an application, we are concerned with Sobolev‐type integral representation for a C1‐function on which vanishes on the unit ball.

Weak Estimates for the Maximal and Riesz Potential Operators in Central Herz–Morrey Spaces on the Unit Ball

Morrey spaces are the powerful tool for the study of partial differential equations. Recently, weak Morrey spaces and weak Herz spaces are known to be useful for the study of Navier–Stokes equations. In this paper we introduce weak central Herz–Morrey spaces W\mathcal H^{p(\cdot),q,\omega}(\mathbf B) and establish the weak estimate for the maximal and Riesz potential operators in the central Herz–Morrey space \mathcal H^{p(\cdot),q,\omega}(\mathbf B) . We also treat generalized Riesz potential operators. Further we obtain the strong estimate for Sobolev functions.

Hardy–Sobolev inequalities for Sobolev functions in central Herz–Morrey spaces on the unit ball

Our aim in this paper is to establish Hardy-Sobolev inequalities for Sobolev functions and generalized Riesz potentials in central Herz-Morrey spaces on the unit ball. As an application, we obtain norm inequalities for Green potentials.

Inclusion Properties of The Homogeneous Herz-Morrey

In this paper, we have discussed about the inclusion properties of the homogeneous Herz-Morrey spaces and the homogeneous weak homogeneous spaces. We also studied the inclusion relation between those spaces.

Hardy’s inequalities and integral operators on Herz-Morrey spaces

Abstract We obtain some estimates for the operator norms of the dilation operators on Herz-Morrey spaces. These results give us the Hardy’s inequalities and the mapping properties of the integral operators on Herz-Morrey spaces. As applications of this general result, we have the boundedness of the Hadamard fractional integrals on Herz-Morrey spaces. We also obtain the Hilbert inequality on Herz-Morrey spaces.

A Characterization of Boundedness of Fractional Maximal Operator with Variable Kernel on Herz-Morrey Spaces

A Characterization of Boundedness of Fractional Maximal Operator with Variable Kernel on Herz-Morrey Spaces

Boundedness of Singular Integral Operators on Herz-Morrey Spaces with Variable Exponent

Let Ω ∈ Ls(Sn−1) (s > 1) be a homogeneous function of degree zero and b be a BMO function or Lipschitz function. In this paper, the authors obtain some boundedness of the Calderon-Zygmund singular integral operator TΩ and its commutator [b, TΩ] on Herz-Morrey spaces with variable exponent.

Hardy and Sobolev inequalities in the half space

Our aim is to establish Hardy and Sobolev inequalities for Sobolev functions in Herz–Morrey spaces, which extend the classical Hardy inequalities in the Lp Lebesgue space.

Boundedness of the maximal and potential operators in Herz-Morrey type spaces

Our aim in this paper is to discuss the boundedness of the maximal and potential operators in the central Herz-Morrey type space for the double phase functional φ such that