Hardy Morrey Spaces Research Articles

Norm Inequalities for Calderón–Zygmund Operators in Some Generalized Hardy–Morrey Spaces

Norm Inequalities for Calderón–Zygmund Operators in Some Generalized Hardy–Morrey Spaces

Calderón–Zygmund operators, Bochner–Riesz means, and parametric Marcinkiewicz integrals on Hardy–Morrey spaces with variable exponents

We obtain the boundedness of Calderón–Zygmund operators on the entire Hardy–Morrey spaces with variable exponents. We obtain this result by refining the extrapolation theory. This refined extrapolation theory also gives the boundedness of Fourier multipliers, Bochner–Riesz means, and parametric Marcinkiewicz integrals on Hardy–Morrey spaces with variable exponents.

$B$-Riesz Transforms Generated by Generalized Translate Operator on $HM^p_{q,{\Delta_{\nu}}}$ Hardy-Morrey Spaces

We study the decomposition of Hardy-Morrey spaces via atoms and molecules, which have similar properties of $H^{p}_{\Delta_{\nu}}(\mathbb{R}^{n}_{+})$ Hardy spaces. Then we introduce the $HM^p_{q,{\Delta_{\nu}}}$ boundedness of $ B $-Riesz transforms generated by a generalized translate operator that is associated to Laplace Bessel operator for $0<p\leq 1<q\leq \infty$ with $p\neq q$ through atomic decomposition and molecular characterization.

Boundedness criterion for some integral operators on generalized mixed Morrey spaces and generalized mixed Hardy–Morrey spaces

Boundedness criterion for some integral operators on generalized mixed Morrey spaces and generalized mixed Hardy–Morrey spaces

Extrapolation to weighted Morrey spaces with variable exponents and applications

AbstractThis paper establishes the mapping properties of pseudo-differential operators and the Fourier integral operators on the weighted Morrey spaces with variable exponents and the weighted Triebel–Lizorkin–Morrey spaces with variable exponents. We obtain these results by extending the extrapolation theory to the weighted Morrey spaces with variable exponents. This extension also gives the mapping properties of Calderón–Zygmund operators on the weighted Hardy–Morrey spaces with variable exponents and the wavelet characterizations of the weighted Hardy–Morrey spaces with variable exponents.

Mixed atomic decomposition of martingale weak Hardy–Morrey spaces

The so-called mixed-type atomic decomposition theorems are established for martingale weak Hardy–Morrey spaces wHMp,ϕs, wHMp,ϕ∗ and wHMp,ϕS, respectively. As applications, a sufficient condition for sublinear operators on martingale weak Hardy–Morrey spaces to be bounded is given. In particular, some classical martingale inequalities, including Burkholder’s inequality, are extended to the case of the weak Morrey space quasi-norms.

Variable martingale Hardy-Morrey spaces

In this paper, we introduce martingale Morrey spaces with variable exponents defined on a probability space. The weak-type and strong-type estimates for the Doob maximal operator on these spaces are established. We also construct the atomic decompositions for variable Hardy-Morrey spaces. As an application of the atomic decompositions, martingale inequalities among different Hardy-Morrey spaces are obtained. Further, we investigate the boundedness of fractional integral operators on martingale Hardy-Morrey spaces.

Hardy’s inequality on Hardy–Morrey spaces

Abstract We generalize the Hardy inequality to Hardy–Morrey spaces.

Generalized Hardy–Morrey Spaces

This paper is an off-spring of the contribution [Z. Anal. Anwend. 36 (2017)(1), 17–35]. We propose a way to consider the decomposition method of generalized Hardy–Morrey spaces. Generalized Hardy–Morrey spaces emerged from generalized Morrey spaces. By means of the grand maximal operator and the norm of generalized Morrey spaces, we can define generalized Hardy–Morrey spaces. With what we have culminated for the Hardy–Littlewood maximal operator, we can easily refine the existing results. As an application, we consider bilinear estimates, which is the "so-called" Olsen inequality. In particular, our results complement the one in the 2014 paper by Iida, the fourth author and Tanaka [Z. Anal. Anwend. 33 (2014)(2), 149–170]; there were two mistakes. One lies in the decomposition result and another lies in the proof of the Olsen inequality.

Hardy’s Inequality on Hardy–Morrey Spaces with Variable Exponents

We obtain a generalization of the Hardy inequality to Hardy–Morrey spaces with variable exponents.

Corrigendum to "Atomic decomposition of Hardy–Morrey spaces with variable exponents"

Corrigendum to "Atomic decomposition of Hardy–Morrey spaces with variable exponents"

Atomic decompositions and Hardy’s inequality on weak Hardy-Morrey spaces

We introduce the weak Hardy-Morrey spaces in this paper. We also obtain the atomic decompositions of the weak Hardy-Morrey spaces. By using these decompositions, we establish the Hardy inequalities on the weak Hardy-Morrey spaces.

Hardy spaces for ball quasi-Banach function spaces

This article unifies the theory for Hardy spaces built on Banach lattices on R-n satisfying certain weak conditions on indicator functions of balls. The authors introduce a new family of function spaces, named the ball quasi-Banach function spaces, to define Hardy type spaces. The ones in this article extend classical Hardy spaces and include various known function spaces, for example, Hardy-Lorentz spaces, Hardy-Herz spaces, Hardy-Orlicz spaces, Hardy-Morrey spaces, Musielak-Orlicz-Hardy spaces, variable Hardy spaces and variable Hardy-Morrey spaces. Among them, Hardy-Herz spaces are shown to naturally arise in the context of any function spaces above. The example of Hardy-Morrey spaces shows that the absolute continuity of the quasi-norm is not necessary, which is used to guarantee the density of the set of functions having compact supports in Hardy spaces for ball quasi-Banach function spaces, but the decomposition result on these Hardy-type spaces never requires this absolute continuity of the quasi-norm. Moreover, via assuming that the powered Hardy-Littlewood maximal operator satisfies certain Fefferman-Stein vector-valued maximal inequality as well as it is bounded on the associate space, the atomic characterizations of Hardy type spaces are obtained. Although the results are based on the rather abstract theory of function spaces, they improve and extend the results for Orlicz spaces and Musielak-Orlicz spaces. Moreover, local Hardy type spaces and Hardy type spaces associated with operators in this setting are also studied.

Atomic decompositions of martingale hardy–morrey spaces

We establish the atomic decompositions of martingale Hardy– Morrey spaces. The martingale Hardy–Morrey spaces are generalizations of martingale Hardy spaces. Therefore, the atomic decompositions presented in this paper are extensions of the atomic decompositions of martingale Hardy spaces.

Fractional Integrals on Variable Hardy–Morrey Spaces

Vector-valued fractional maximal inequalities on variable Morrey spaces are proved. Applying atomic decomposition of variable Hardy–Morrey spaces, we obtain the boundedness of fractional integrals on variable Hardy–Morrey spaces, which extends the Taibleson–Weiss’s results for the boundedness of fractional integrals on Hardy spaces. The corresponding boundedness for the fractional type integrals is also considered.

Atomic decomposition of Hardy-Morrey spaces with variable exponents

The Hardy-Morrey spaces with variable exponents are introduced in terms of maximal functions. The atomic decomposition of Hardy-Morrey spaces with variable exponents is established. This decomposition extends and unifies several atomic decompositions of Hardy type spaces such as the Hardy-Morrey spaces and the Hardy spaces with variable exponents. Some applications of this atomic decomposition on singular integral are presented.

Atomic decompositions of weighted Hardy-Morrey spaces

We obtain the Fefferman-Stein vector-valued maximal inequalities on Morrey spaces generated by weighted Lebesgue spaces. Using these inequalities, we introduce and define the weighted Hardy-Morrey spaces by using the Littlewood-Paley functions. We also establish the non-smooth atomic decompositions for the weighted Hardy-Morrey spaces and, as an application of the decompositions, we obtain the boundedness of a class of singular integral operators on the weighted Hardy-Morrey spaces.

A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.

Decomposition of Hardy–Morrey spaces

In this paper, we establish the decompositions of Hardy–Morrey spaces in terms of atoms concentrated on dyadic cubes, which have the same cancellation properties of the classical Hardy spaces.