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1

On the Besov regularity of the Bifractional Brownian motion

Boufouss Brahim, Nachit Yassine

Probability and Mathematical Statistics

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2021

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Vol. 41, Fasc. 2

303--320

EN

Our aim is to improve Hölder continuity results for the bifractional Brownian motion (bBm) (Bα,β(t))t∈[0,1] with 0 < α < 1 and 0 < β ≤ 1. We prove that almost all paths of the bBm belong to (resp. do not belong to) the Besov spaces Bes(αβ,p) (resp. bes(αβ,p)) for any 1/αβ < p < ∞, where bes(αβ,p) is a separable subspace of Bes(αβ,p). We also show similar regularity results in the Besov-Orlicz space Bes(αβ, M2) with M2(x) = ex2 −1. We conclude by proving the Itô-Nisio theorem for the bBm with αβ > 1/2 in the Hölder spaces Cγ with γ < αβ.

2

On the deformed Besov-Hankel spaces

Said Salem Ben, Boubatra Mohamed Amine, Sifi Mohamed

Opuscula Mathematica

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2020

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Vol. 40, no. 2

171--207

EN

In this paper we introduce function spaces denoted by [formula] as subspaces of Lp that we call deformed Besov-Hankel spaces. We provide characterizations of these spaces in terms of Bochner-Riesz means in the case 1 ≤ p ≤ +∞ and in terms of partial Hankel integrals in the case 1 < p < +∞ associated to the deformed Hankel operator by a parameter k > 0. For p = r = +∞, we obtain an approximation result involving partial Hankel integrals.

3

Generalized weighted Besov spaces on the Gegenbauer hypergroup

Ibrahimov E. J.

Commentationes Mathematicae

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2014

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Vol 54, No. 1

95--128

EN

In this paper we study generalized weighted Besov type spaces on the Gegenbauer hypergroup. We give different characterizations of these spaces in terms of generalized convolution with a kind of smooth functions and by means of generalized translation operators. Also a discrete norm is given to obtain more general properties on these spaces. Obtained results are analogies of the results for generalized Bessel shifts obtained in the work [5].

4

Remark on borderline traces of Besov and Triebel-Lizorkin spaces on noncompact hypersurfaces

Skrzypczak L., Tomasz B.

Commentationes Mathematicae

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2013

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Vol. 53, No. 2

193--209

EN

We investigate borderline traces of Besov and Triebel-Lizorkin spaces. The function spaces are defined on noncompact Riemannian manifolds with bounded geometry. We described spaces of traces on noncompact submanifolds that are also of bounded geometry.

5

Characterizations of some function spaces in terms of Haar wavelets

Triebel H.

Commentationes Mathematicae

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2013

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Vol. 53, No. 2

35--53

EN

Some spaces Asp,q(Rn) with A = {B, F}, s ϵ R, 0 < p, q ≤ ∞, covering Besov spaces, Hölder-Zygmund spaces and Sobolev spaces, admit characterizations in terms of Haar bases. It is the main aim of this paper to extend this observation to corresponding Morreyfied spaces Lr Asp,q(Rn). As a by-product we obtain Littlewood-Paley theorems for (homogeneous and inhomogeneous) Morrey spaces Lrp(Rn), Lrp(Rn) and, in particular, L°rp(Rn).

6

Finite difference equations and convergence rates in the central limit theorem

Lindhagen L.

Probability and Mathematical Statistics

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2007

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Vol. 27, Fasc. 2

153--166

EN

We apply the theory of finite difference equations to the central limit theorem, using interpolation of Banach spaces and Fourier multipliers. Let S*n be a normalized sum of i.i.d. random vectors, converging weakly to a standard normal vector N. When does ǁEg (x + S*n) -E g (X + N)ǁLp(dx)tend to zero at a specified rate? We show that, under moment conditions, membership of g in various Besov spaces is often sufficient and sometimes necessary. The results extend to signed probability.

7

The regularity of measures and related properties of eigenfunctions and first eigenvalues of some fractal elliptic operators

Triebel H.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2004

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Vol. 44, nr spec.

257-283

EN

The paper deals with regularity properties of potentials of Radon measures u in IR^n, expressed in terms of some fractal quantities of u (Theorem 1). Based on these assertions, first eigenvalues and eigenfunctions of some fractal elliptic operators are considered (Theorems 2 and 3). The results are illustrated by examples.