Related papers: A dual representation theorem on the conditional O…
Noting the important role the abstract $L^p$ space has played in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a random normed module. First, we give a basic dual space…
In this paper, we give Poisson and Cauchy representation theorems in Hardy-Orlicz spaces on the upper complex half-plane. We use these theorems for the construction of dual spaces of certain Hardy-Orlicz spaces and also for the…
Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional K\"{o}the dual of an Orlicz-type module as the space of all $\sigma$-order…
This article generalize the classical Goldstine-Weston theorem on normed spaces to one on random normed modules: the image of a random normed module $(E,\|\cdot\|)$ under the random natural embedding $J$ is dense in its double random…
In this article we develop the theory of $H$-Orlicz space generated by generalised Young function. Modular convergence of $H$-Orlicz space for the case of vector-valued functions and norm convergence in $\mcH^\theta(X, \bar{\mu})$ where $X$…
We prove the density of smooth functions in the modular topology in the Musielak-Orlicz-Sobolev spaces essentially extending the results of Gossez \cite{GJP2} obtained in the Orlicz-Sobolev setting. We impose new systematic regularity…
In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem established following a density approach. To do this, a Luxemburg…
For an Orlicz function $\varphi$ and a decreasing weight $w$, two intrinsic exact descriptions are presented for the norm in the K\"othe dual of an Orlicz-Lorentz function space $\Lambda_{\varphi,w}$ or a sequence space…
The aim of this article is to prove a representation theorem for orthogonally additive polynomials in the spirit of the recent theorem on representation of orthogonally additive polynomials on Banach lattices but for the setting of Riesz…
We give sufficient conditions for the continuity in norm of the translation operator in the Musielak-Orlicz LM spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the…
For a measure space $\Omega$ we extend the theory of Orlicz spaces generated by an even convex integrand $\varphi \colon \Omega \times X \to \left[ 0, \infty \right]$ to the case when the range Banach space $X$ is arbitrary. Besides…
Given an Orlicz function $M$, we show which random variables $\xi_i$, $i=1,...,n$ generate the associated Orlicz norm, i.e., which random variables yield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_i\xi_i| \sim \norm{(x_i)_{i=1}^n}_M$. As a…
The primary contribution of this study lies in proposing a new concept termed $2$-tuples of noncommutative Orlicz sequence spaces $\bigoplus\limits_{j=1}^{2}S_{\varphi_{j},p}$, where $S_{\varphi_{j}}$ denotes a noncommutative Orlicz…
Here we provide a unifying treatment of the convergence of a general form of sampling type operators, given by the so-called Durrmeyer sampling type series. In particular we provide a pointwise and uniform convergence theorem on…
In the article we generalize the Marcinkiewicz sampling theorem in the context of Orlicz spaces. We establish conditions under which sampling theorem holds in terms of restricted submultiplicativity and supermultiplicativity of an…
Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double…
We introduce a generalized version of Orlicz premia, based on possibly non-convex loss functions. We show that this generalized definition covers a variety of relevant examples, such as the geometric mean and the expectiles, while at the…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
In this paper we consider composition operator $C_{\varphi} generated by nonsingular measurable transformation $T$ and multiplication operator $M_u$ generated by measurable function $u$ between two different Orlicz spaces, then we…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…