相关论文: Differentiating Orlicz spaces with rare bases of r…
We show that, given some lacunary sequence of angles $\mathbf{\theta}=(\theta_j)_{j\in\N}$ not converging too fast to zero, it is possible to build a rare differentiation basis $\mathcal{B}$ of rectangles parallel to the axes that…
In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectangle to belong to the basis, the ratio of the largest of its…
We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces. We find also…
The approximation of functions in Orlicz space by multivariate operators on simplex is considered. The convergence rate is given by using modulus of smoothness.
In this paper we discuss the structure of Orlicz spaces and weak Orlicz spaces on $\mathbb{R}^n$. We obtain some necessary and sufficient conditions for the inclusion property of these spaces. One of the keys is to compute the norm of the…
The purpose of this paper is to introduce the space of geometric sequences that are strongly summable with respect to an Orlicz function and the Fibonacci difference sequences.Also some topological properties and inclusion relations between…
We propose and analyze a randomized zeroth-order approach based on approximating the exact gradient byfinite differences computed in a set of orthogonal random directions that changes with each iteration. A number ofpreviously proposed…
This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…
We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms.…
In this work we investigate families of translation invariant differentiation bases $B$ of rectangles in $R^n$, for which $L\log^{n-1}L(R^n)$ is the largest Orlicz space that $B$ differentiates. In particular, we improve on techniques…
We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. The construction is applied in two settings. First, we show…
In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in $\mathbb{R}^{2}$ are defined and studied. This family of norms includes the family of the p-Amemiya norms ($1\leq p\leq\infty$)…
We explore the separability of point sets in the plane by a restricted-orientation convex hull, which is an orientation-dependent, possibly disconnected, and non-convex enclosing shape that generalizes the convex hull. Let $R$ and $B$ be…
In this current study, the most apparent aspect is to submit a new geometric sequence space. We investigate its topological properties , inclusion relations, Geometric statistical convergence and Geometric property of Orlicz function and .…
The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications of a full convergence $\mathbb{c}$ on a Riesz space. The first…
In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces.…
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $\mathbb R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all…
The Erd\H{o}s distinct distance problem is a ubiquitous problem in discrete geometry. Somewhat less well known is Erd\H{o}s' distinct angle problem, the problem of finding the minimum number of distinct angles between $n$ non-collinear…
We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper…
The criterion for a point in the unit ball to be a strongly exposed point is given. The necessity and sufficiency conditions for Orlicz-Lorentz spaces to possess strongly exposed property are given. Besides, some useful methods are obtained…