Related papers: Continuity of conditional expectation in Orlicz sp…
A necessary and sufficient condition on a sequence $\{\mathfrak{A}_n\}_{n\in \mathbb{N}}$ of $\sigma$-subalgebras that assures convergence almost every where of conditional expectations is given.
We find conditions on a function space $\bf{L}$ that ensure that it behaves as an $L_p$-space in the sense that any unconditional basis of a complemented subspace of $\bf{L}$ either is equivalent to the unit vector system of $\ell_2$ or has…
A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into $L^\infty(\mathbb R^n)$ is exhibited. Under the same assumption, any function from the relevant fractional-order spaces is shown to…
In this paper we consider a generalized conditional-type Holder- inequality and investigate some classic properties of multiplication conditional expectation type operators on Orlicz-spaces.
Necessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on $\rn$ to be continuously embedded into a space of uniformly continuous functions. The optimal modulus of continuity is exhibited whenever these…
The concept of reiterated $\Sigma$-convergence (and more generally of multiscale $\Sigma$-convergence) is extended to framework of Orlicz-Sobolev spaces, in order to deals with homogenization of multiscales problems in general deterministic…
In this paper we investigate the conditional expectation on the non-commutative $H^{(r,s)}_{p}(\mathcal A;\ell_{\infty})$ and $H_{p}(\mathcal A;\ell_{1})$ spaces associated with semifinite subdiagonal algebra, and prove the contractibility…
Orlicz spaces are generalizations of Lebesgue spaces. The sufficient and necessary conditions for generalized H\"{o}lder's inequality in Lebesgue spaces and in weak Lebesgue spaces are well known. The aim of this paper is to present…
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…
The continuity of the Nemytskii operator between Orlicz-Sobolev spaces is investigated. Natural Orlicz-Sobolev versions of classical results for standard Sobolev are established. The results presented not only extend the latter, but also…
Let $(A,\mathscr{A},\mu)$ and $(B,\mathscr{B},\nu)$ be probability spaces, let $\mathscr{F}$ be a sub-$\sigma$-algebra of the product $\sigma$-algebra $\mathscr{A}\times\mathscr{B}$, let $X$ be a Banach space, and let $1< p,q< \infty$. We…
We deal with Orlicz-Sobolev embeddings in open subsets of $\mathbb{R}^n$. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given…
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a…
In this article we introduce a new scale of weighted Orlicz-Sobolev sequence spaces generated by a class of suitable Orlicz functions and prove various continuity and compactness criteria for them. In a nutshell, continuity is a consequence…
Let $G$ be an Orlicz function and let $ \alpha, \beta, s$ be positive real numbers. Under certain conditions on the Orlicz function $ G $, we establish some continuous embeddings results between the fractional order Orlicz-Sobolev spaces…
In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…
Let (f_n) and (g_n) be two sequences of random variables adapted to an increasing sequence of $\sigma$-algebras $({\cal F}_n)$ such that the conditional distributions of f_n and g_n given ${\cal F}_{n-1}$ coincide, and such that the…
Strong convergence and convergence in probability were generalized to the setting of a Riesz space with conditional expectation operator, $T$, in [{{\sc Y. Azouzi, W.-C. Kuo, K. Ramdane, B. A. Watson}, {Convergence in Riesz spaces with…
In this paper we prove the existence of conditional expectations in the noncommutative $L_p(M,\Phi)$ spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we…
In this paper we study some basic properties, like boundedness and closedness of range, of multiplication conditional expectation(MCE) operators between different Orlicz spaces.