Related papers: Besov regularity in non-linear generalized functio…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
The canonical generalizations of two classical norms on Besov spaces are shown to be equivalent even in the case of non-linear Besov spaces, that is, function spaces consisting of functions taking values in a metric space and equipped with…
We give a new description of classical Besov spaces in terms of a new modulus of continuity. Then a similar approach is used to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure.
We introduce and analyze spaces and algebras of generalized functions which correspond to H\" older, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are…
This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…
The theory of regularity structures sets up an abstract framework of modelled distributions generalising the usual H\"older functions and allowing one to give a meaning to several ill-posed stochastic PDEs. A key result in that theory is…
We establish conditions on the parameters which are both necessary and sufficient in order that Besov and Triebel-Lizorkin spaces of generalized smoothness contain only regular distributions. We also connect this with the possibility of…
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…
We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…
We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good…
Motivated by the study of the distribution of zeros of generalized Bessel-type functions, the principal goal of this paper is to identify new research directions in the theory of multiplier sequences. The investigations focus on multiplier…
We prove that continuous paths of \sigma-additive in probability set function belong to Besov space.
We investigate Besov spaces of self-affine tilings of ${\Bbb R}^{n}$ and discuss various characterizations of those Besov spaces. We see what is a finite set of functions which generates the Besov spaces from a view of multiresolution…
We introduce and investigate classes of normed or quasinormed distribution spaces of generalized smoothness that can be obtained by various interpolation methods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkin spaces. An…
A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are H\"older spaces and Sobolev…
Our main purpose is to use a new condition, $\alpha$-local nondeterminism, which is an alternative to the classical local nondeterminism usually utilized in the Gaussian framework, in order to investigate Besov regularity, in the time…
We study fractional smoothness of measures on $\mathbb{R}^k$, that are images of a Gaussian measure under mappings from Gaussian Sobolev classes. As a consequence we obtain Nikolskii--Besov fractional regularity of these distributions under…
The article examines Nikolskii and Besov spaces with norms defined using $L_p$-averaged mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative…
We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. We show that the various constructions of such embeddings existing in the literature lead in fact to the same…
We prove embedding theorems for fully anisotropic Besov spaces. More concrete, inequalities between modulus of continuity in different metrics and of Sobolev type are obtained. Our goal is to get sharp estimates for some anisotropic cases…