on spaces of homogeneous type: a density result on - spaces.
spaces and rectifiability for Carnot-Carathéodory metrics: an introduction
This paper is meant as a (short and partial) introduction to the study of the geometry of Carnot groups and, more generally, of Carnot-Carathéodory spaces associated with a family of Lipschitz continuous vector fields. My personal interest in this field goes back to a series of joint papers with E. Lanconelli, where this notion was exploited for the study of pointwise regularity of weak solutions to degenerate elliptic partial differential equations. As stated in the title, here we are mainly concerned...
Balls defined by nonsmooth vector fields and the Poincaré inequality
We provide a structure theorem for Carnot-Carathéodory balls defined by a family of Lipschitz continuous vector fields. From this result a proof of Poincaré inequality follows.
Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions. Part II.
Basic compactness properties of nonconforming and hybrid finite element spaces
Basic properties of Sobolev's spaces on time scales.
Basic relations valid for the Bernstein spaces and their extensions to larger function spaces via a unified distance concept
Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from . The difficult situation of derivative-free error estimates is also covered.
Berezin and Berezin-Toeplitz quantizations for general function spaces.
The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic...
Besov and Triebel-Lizorkin spaces related to singular integrals with flag kernels.
Besov capacity and Hausdorff measures in metric measure spaces.
Besov characteristic of a distribution.
Besov spaces and 2-summing operators
Let Π₂ be the operator ideal of all absolutely 2-summing operators and let be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also consider the...
Besov spaces and function series on Lie groups.
Besov spaces and function series on Lie groups
In the paper we investigate the absolute convergence in the sup-norm of Harish-Chandra's Fourier series of functions belonging to Besov spaces defined on non-compact connected Lie groups.
Besov spaces and function series on Lie groups (II).
In this paper we investigate the absolute convergence in the sup-norm of two-sided Harish-Chandra's Fourier series of functions belonging to Zygmund-Hölder spaces defined on non-compact connected Lie groups.[Part I of the article in MR1240211].
Besov spaces and the boundedness of weighted Bergman projections over symmetric tube domains.
Besov spaces on local fields
Besov spaces on spaces of homogeneous type and fractals
Let Γ be a compact d-set in ℝⁿ with 0 < d ≤ n, which includes various kinds of fractals. The author shows that the Besov spaces defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding Γ as a space of homogeneous type when 0 < s < 1, 1 < p < ∞ and 1 ≤ q ≤ ∞.
Besov spaces on surfaces with singularities.
Besov spaces on symmetric manifolds—the atomic decomposition
We give the atomic decomposition of the inhomogeneous Besov spaces defined on symmetric Riemannian spaces of noncompact type. As an application we get a theorem of Bernstein type for the Helgason-Fourier transform.