Herz-Morrey Spaces Research Articles

Commutators of the Bilinear Hardy Operator on Herz Type 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 Herz spaces and Herz-Morrey spaces with variable exponents.

Weak estimates for the maximal and Riesz potential operators in non-homogeneous central Herz-Morrey spaces

ABSTRACTOur aim in this paper is to discuss the weak estimate for the maximal and Riesz potential operators in the non-homogeneous central Morrey type space . Further we obtain the strong estimate for Sobolev functions.

Boundedness of some sublinear operators on weighted variable Herz-Morrey spaces

Boundedness of some sublinear operators on weighted variable Herz-Morrey spaces

Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball

Our aim in this paper is to establish variable exponent weighted norm inequalities for generalized Riesz potentials on the unit ball via norm inequalities in variable exponent non-homogeneous central Herz–Morrey spaces on the unit ball. As an application, we shall show Sobolev-type integral representation for a ?1 -function on ℝ?∖{0} which vanishes outside the unit ball.

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.

A vector-valued estimate of multilinear Calderón-Zygmund operators in Herz-Morrey spaces with variable exponents

In this paper, we obtain a vector valued inequality of multilinear Calderon-Zygmund operators on products of Herz-Morrey spaces with variable exponents.

Boundedness for fractional Hardy-type operator on variable-exponent Herz–Morrey spaces

In this article, the fractional Hardy-type operator of variable order β(x) is shown to be bounded from the variable-exponent Herz–Morrey spaces MK˙p1,q1(⋅)α(⋅),λ(Rn) into the weighted space MK˙p2,q2(⋅)α(⋅),λ(Rn,ω), where α(x)∈L∞(Rn) is log-Hölder continuous both at the origin and at infinity, ω=(1+|x|)−γ(x) with some γ(x)>0, and 1/q1(x)−1/q2(x)=β(x)/n when q1(x) is not necessarily constant at infinity.

The Boundedness of Fractional Integral with Variable Kernel on Variable Exponent Herz-Morrey Spaces

In this paper, we study the boundedness of the fractional integral with variable kernel. Under some assumptions, we prove that such kind of operators is bounded from the variable exponent Herz-Morrey spaces to the variable exponent Herz-Morrey spaces.

Boundedness of Littlewood-Paley operators and their commutators on Herz-Morrey spaces with variable exponent

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and -functions, and their commutators on the Herz-Morrey spaces with variable exponent . By applying the properties of spaces and the vector-valued inequalities for Littlewood-Paley operators and their commutators generated by BMO function on , the boundedness of the vector-valued Littlewood-Paley operators and their commutators is obtained on . MSC:42B20, 42B25, 42B35.

Herz–Morrey spaces of variable exponent, Riesz potential operator and duality

Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator on Herz–Morrey spaces and to establish Sobolev’s inequalities for Riesz potentials of functions in Herz–Morrey spaces. Further, we discuss the associate spaces among Herz–Morrey spaces.

A class of subspaces of Morrey spaces and norm inequalities on Riesz potential operators

We introduce two classes of Banach spaces $$F(q,p,\alpha )$$ and $$T^{p,\;\alpha }$$ ( $$1\le q\le \alpha \le p\le \infty $$ ) which are subspaces of Herz spaces and Morrey spaces of functions and measures respectively. We study the Riesz potential operators in these spaces and obtain norm inequalities on these operators from which we deduce a necessary condition for a nonnegative Radon measure to have its Riesz potential in a given Lebesgue space.

Boundedness of some sublinear operators on Herz–Morrey spaces with variable exponent

Abstract. In this paper, the boundedness of some sublinear operators is proved on homogeneous Herz–Morrey spaces with variable exponent.

Sobolev's theorem and duality for Herz-Morrey spaces of variable exponent

In this paper, we consider the Herz-Morrey space H p(·),q,! {x0} (G) of variable exponent consisting of all measurable functions f on a bounded open set G ⊂ R n satisfying kfk H p(·),q,! {x0} (G) = ˆ 2dG H p(·),q,! (G),H p(·),q,! {x0} (G) and ˜ H p(·),q,! (G). Following Fiorenza-Rakotoson (18), Di Fratta-Fiorenza (17) and Gogatishvili-Mustafayev (19), we next discuss the duality properties among these Herz- Morrey spaces.

Boundedness for commutators of fractional integrals on Herz–Morrey spaces with variable exponent

In this paper, some boundedness for commutators of fractional integrals is obtained on Herz–Morrey spaces with variable exponent applying some properties of variable exponent and bounded mean oscillation (BMO) functions.

Commutators of Multilinear Calderón-Zygmund Operator and BMO Functions in Herz-Morrey Spaces with Variable Exponents

We obtain the boundedness of a commutator generated by multilinear Calderón-Zygmund operator and BMO functions in Herz-Morrey spaces with variable exponents.

On the Boundedness of Multilinear Operators on Weighted Herz-Morrey Spaces

Boundedness of multilinear operators on weighted Herz-Morrey spaces is established in this paper. The weak estimates on endpoints are also derived. As a special case, the conclusions can apply to multilinear Calderón-Zygmund operators.

Sharp Maximal Inequalities and Its Application to Some Bilinear Estimates

In this note we establish the sharp maximal inequalities for Herz spaces and Morrey spaces by use of good λ-inequality. As an application, we obtain estimates of some bilinear forms which include usual product of functions and the nonlinear term of Euler and Navier-Stokes equations on Herz spaces and Morrey spaces.

Boundedness for multilinear fractional integral operators on Herz type spaces

In this paper the boundedness for the multilinear fractional integral operator Iα(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy-Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.