Commutators of a class of $Ψ$-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications

Fate Shan; Jiang Zhou

Home/Archive/arXiv

arXiv · 2608.25517

Commutators of a class of $Ψ$-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications

Fate Shan·Jiang Zhou

View original source ↗Read source document ↗Export metadata ↓

Abstract

In our previous work \cite{SZ2026}, we established a class of abstract Orlicz-Morrey spaces endowed with a ball-basis and introduced the notion of $Ψ$-bounded oscillation operators. The present paper further develops this theory by investigating sparse domination and weighted estimates for such operators and their commutators within the framework of abstract Orlicz-Morrey spaces endowed with a ball-basis. We obtain pointwise sparse domination results for the operators and establish their boundedness on weighted Orlicz-Morrey spaces. The hypotheses of these conclusions differ from those in the classical Orlicz-Morrey setting and do not rely on dyadic decompositions of Euclidean structure. Moreover, we study the duality of these spaces and prove that the dual of the associated block space is exactly the Orlicz-Morrey space under consideration.

Explore related subjects

math.FA

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Fate Shan, Jiang Zhou. 2026-08-26. Commutators of a class of $Ψ$-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications. https://arxiv.org/abs/2608.25517

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Complex Geometric Approach to the Discrete Gabor Transform and Localization Operators on the Flat Torus

In a recent paper, the discrete Gabor transform was connected to a Gabor transform with a time frequency domain given by the flat torus. We show that the corresponding Bargmann-Fock spaces can be expressed as theta functions (or equivalently line bundles on Abelian varieties). We give applications of this viewpoint to frame results for the discrete Gabor transform. In particular, we get necessary conditions which hold in higher dimensions and can expand the known results in the one dimensional case, the primary tool being the theorem of the square. We also give an application to asymptotics of restriction operators which arises via the asymptotic behavior of Bergman kernels and Toeplitz operators for high tensor powers of line bundles and find that time frequency restriction operators on the flat torus will exhibit "plunge" behaviors similar to those of time frequency restriction operators in other contexts.

math.FA↗

arXiv2026

On a minimal Andô dilation for a pair of strict contractions

The isometric dilation of a pair of commuting contractions due to Andô is not minimal. We modify Andô's dilation and construct a minimal isometric dilation on $\mathcal H \oplus_2 \ell_2(\mathcal H \oplus_2 \mathcal H)$ for a commuting pair of strict contractions on a Hilbert space $\mathcal H$. In the same spirit, we construct under certain conditions a minimal Andô dilation for a commuting pair of strict Banach space contractions. Further, we show that an Andô dilation is possible even for a more general pair of commuting contractions $(T_1,T_2)$ on a normed space $\mathbb X$ provided that the function $A_{T_i}: \mathbb X \rightarrow \mathbb R$ given by $A_{T_i}(x)=(\|x\|^2-\|T_ix\|^2)^{\frac{1}{2}}$ defines a norm on $\mathbb X$ for $i=1,2$.

math.FA↗

arXiv2026

Some properties of Fourier quasicrystals and measures on a strip

We extend certain results of the theory of Fourier quasicrystals on the real line to the case of a horizontal strip of finite width. For measures in a strip we use a natural generalization of the usual Fourier transform for measures on the line. We consider positive or translation bounded measures $μ$ on a strip whose Fourier transform is a pure point measure $\hatμ=\sum_{γ\inΓ}b_γδ_γ$ (as usual, $δ_γ$ is the unit mass at the point $γ$). We prove that the measure $ν=\sum_{γ\inΓ}|b_γ|^2δ_γ$ has the exponential growth. Moreover, if for some $η>0$ the points of $Γ$ in every interval of length $η$ are linearly independent over integers, then the measure $\hatμ$ also has the exponential growth.

math.FA↗