Twisted sums, Fenchel-Orlicz spaces and property (M)

Complex interpolation of Orlicz sequence spaces and its higher order Rochberg spaces

We show that if $(\ell_{ϕ_0}, \ell_{ϕ_1})$ is a couple of suitable Orlicz sequence spaces then the corresponding Rochberg derived spaces of all orders associated to the complex interpolation method are Fenchel-Orlicz spaces. In particular, the induced twisted sums have the $(C[0, 1], \mathbb{C})$-extension property.

Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces

Let $\mathbb{Y}$ be either an Orlicz sequence space or a Marcinkiewicz sequence space. We take advantage of the recent advances in the theory of factorization of the identity carried on in [R. Lechner, Subsymmetric weak* Schauder bases and factorization of the identity, arXiv:1804.01372 [math.FA]] to provide conditions on $\mathbb{Y}$ that ensure that, for any $1\le p\le\infty$, the infinite direct sum of $\mathbb{Y}$ in the sense of $\ell_p$ is a primary Banach space, enlarging this way the list of Banach spaces that are known to be primary.

Non-separably valued Orlicz spaces, part I

For a measure space $Ω$ we extend the theory of Orlicz spaces generated by an even convex integrand $φ\colon Ω\times X \to \left[ 0, \infty \right]$ to the case when the range Banach space $X$ is arbitrary. Besides settling fundamental structural properties such as completeness, we characterize separability, reflexivity and represent the dual space. This representation includes the cases when $X'$ has no Radon-Nikodym property or $φ$ is unbounded. We apply our theory to represent convex conjugates and Fenchel-Moreau subdifferentials of integral functionals, leading to the first general such re…

Orlicz空间松弛的全变分去噪

Orlicz space relaxation of total variation denoising

本文提出一种基于Orlicz空间松弛的全变分去噪模型，通过对数密度校正减少阶梯效应，并证明其收敛到ROF模型。

关于满足Hoffmann-Jørgensen不等式的Orlicz空间

On Orlicz spaces satisfying the Hoffmann-Jørgensen inequality

本研究基于Talagrand的相关证明，完整刻画了满足Hoffmann-Jørgensen型不等式的Orlicz函数，推广了多类集中不等式与有界性结论。

Köthe-Herz空间：无限直和的融合型空间

Köthe-Herz Spaces: The Amalgam-Type Spaces of Infinite Direct Sums

本文引入Köthe-Herz空间$E(\mathcal{X})$，一种融合型无限直和函数空间，研究其几何拓扑性质，给出Banach函数空间刻画，并通过融合Lorentz与Orlicz空间定义Herz型空间，证明插值结果与次线性积分算子有界性。