相关论文: Bounding the Cebysev Functional for Sequences of V…
Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.
In this paper, we study a part of approximation theory that presents the conditions under which a closed set in a normed linear space is proximinal or Chebyshev.
In this paper several new bounds for the \v{C}eby\v{s}ev functional involving $L_p$-norm are presented.
This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…
This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalised weakly differentiable functions and share key functional…
A theory of $\infty$-Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the $\infty$-Besov semi-norms, we obtain new restriction-extension inequalities and…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized function spaces. We obtain precise…
We introduce Besov and Triebel--Lizorkin spaces on a manifold with boundary adapted to H\"ormander vector fields, near a so-called non-characteristic point of the boundary. We prove sharp results in these spaces for the corresponding…
We deduce an extension theorem for the so-called Sobolev-Grand Lebesgue Spaces defined on the suitable subsets of the whole finite-dimensional Euclidean space, and estimate the norms of correspondent extension operator, which may be choosed…
The aim of this paper is to prove a trace theorem for Besov functions in the metric setting, generalizing a known result from A. Jonsson and H. Wallin in the Euclidean case. We show that the trace of a Besov space defined in a `big set' $X$…
Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of…
The motivation of this paper is a suggestion by H\"ole of comparing the notions of $\D$-boundedness and boundedness in Probabilistic Normed spaces (briefly PN spaces), with non necessarily continuous triangle functions. Such spaces are here…
In the paper, the basic results on boundary trace of the book "Sobolev spaces" by V. Maz'ya are generalized to a wider class of regions. In the book, boundary trace of BV-functions is defined for regions with finite perimeter and the main…
In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that…
We study the boundary traces of Newton-Sobolev, Hajlasz-Sobolev, and BV (bounded variation) functions. Assuming less regularity of the domain than is usually done in the literature, we show that all of these function classes achieve the…
In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization.