Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.19745

Continuous and compact embeddings for a class of modular sequence spaces

Pierre-A. Vuillermot
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this article we prove the existence of continuous and compact embeddings for a class of modular sequence spaces generated by Orlicz functions. The class under consideration contains sequence spaces of Orlicz-Sobolev type, including certain special cases that have played an important role in a number of applications regarding problems arising in non-equilibrium statistical mechanics, as well as Nakano's class of Lebesgue sequence spaces with variable exponents. In a few exceptional cases we provide necessary and sufficient conditions for such embeddings to hold, in many others only sufficient conditions and in that situation we clearly indicate why these are not necessary by means of additional criteria and specific examples. Our results are complementary to those already available in the literature. We illustrate them with several concrete examples.

Explore related subjects

math.FA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pierre-A. Vuillermot. 2026-10-14. Continuous and compact embeddings for a class of modular sequence spaces. https://arxiv.org/abs/2610.19745

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

KEEP EXPLORING

Related papers

arXiv2026

Non-Archimedean Heisenberg-Robertson-Schrodinger and Non-Archimedean Maccone-Pati Uncertainty Principles

Let $\mathcal{X}$ be a non-Archimedean Hilbert space over a conjugated non-Archimedean valued field $\mathbb{K}$ with $\operatorname{Char}(\mathbb{K})\neq 2$. Let $A: \mathcal{D}(A)\subseteq \mathcal{X}\to \mathcal{X}$ and $B: \mathcal{D}(B)\subseteq \mathcal{X}\to \mathcal{X}$ be possibly unbounded self-adjoint linear operators. For $x \in \mathcal{D}(A)$ with $\langle x, x \rangle =1$, define $ Δ_x(A):= \|Ax- \langle Ax, x \rangle x \|.$ Then for all $x \in \mathcal{D}(AB)\cap \mathcal{D}(BA)$ with $\langle x, x \rangle =1$, we show that \begin{align*} (1) \quad Δ_x(A)+Δ_x(B)\geq \max\{Δ_x(A), Δ_x(B)\}\geq \frac{\sqrt{\bigg|\big\langle [A,B]x, x \big\rangle ^2+\big(\langle \{A,B\}x, x \rangle -2\langle Ax, x \rangle\langle Bx, x \rangle\big)^2\bigg|}}{\sqrt{|2|}} \end{align*} and \begin{align*} (2) \quad Δ_x(A)+Δ_x(B)\geq \max\{Δ_x(A), Δ_x(B)\} \geq |\langle (A+B)x, y \rangle |, \quad \forall y \in \mathcal{X} \text{ satisfying } \|y\|\leq 1, \langle x, y \rangle =0. \end{align*} Inequality (1) may be regarded as a non-Archimedean analogue of the Heisenberg-Robertson-Schrodinger uncertainty principle, while Inequality (2) serves as a non-Archimedean analogue of the Maccone-Pati uncertainty principle.

math.FA↗
arXiv2026

Divergence Liftings and Regular Factorizations for Metric Cotype

The least regular norm of a factorization of antipodal differences through sign differences on \((\mathbb Z/m\mathbb Z)^n\) is \(m/2\) when \(4\mid m\). On these tori, when \(2\sqrt n\le m\le4\sqrt n\), normalized divergence equations admit selections with pointwise norm bound \(3/2\), while the least linear lifting norm and global Lipschitz selection constant equal \(\sqrt n/2\). Higher-moment lifting bounds follow from a quoted sharp \(L_1\) inequality.

math.FA↗
arXiv2026

The Critical Value for the Beurling-Type Theorem in Weighted Bergman Spaces

For every $α>1$ we construct a finite set $A\subset\mathbb{D}$ such that the zero-based invariant subspace $I_A$ fails the wandering subspace property. Consequently, the Beurling-type theorem holds on the weighted Bergman space $A^2_α$ if and only if $-1<α\le1$, confirming a conjecture of Shimorin. As a further application, we extend the prescribed-curvature construction of Hedenmalm and Perdomo to all $α>1$, thereby replacing the constant $α_0\approx1.04$ in their result by $1$.

math.FA↗