منابع مشابه
Calderón-zygmund Capacities and Wolff Potentials on Cantor Sets
We show that, for some Cantor sets in R, the capacity γs associated to the s-dimensional Riesz kernel x/|x| is comparable to the capacity Ċ 2 3 (d−s), 3 2 from non linear potential theory. It is an open problem to show that, when s is positive and non integer, they are comparable for all compact sets in R. We also discuss other open questions in the area.
متن کاملCantor sets
This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...
متن کاملMulti-Model Cantor Sets
In this paper we define a new class of metric spaces, called multimodel Cantor sets. We compute the Hausdorff dimension and show that the Hausdorff measure of a multi-model Cantor set is finite and non-zero. We then show that a bilipschitz map from one multi-model Cantor set to another has constant Radon-Nikodym derivative on some clopen. We use this to obtain an invariant up to bilipschitz hom...
متن کاملEquilibrium Cantor-type Sets
Equilibrium Cantor-type sets are suggested. This allows to obtain Green functions with various moduli of continuity and compact sets with preassigned growth of Markov’s factors.
متن کاملParabolic Cantor sets
The notion of a parabolic Cantor set is introduced allowing in the definition of hyperbolic Cantor sets some fixed points to have derivatives of modulus one. Such difference in the assumptions is reflected in geometric properties of these Cantor sets. It turns out that if the Hausdorff dimension of this set is denoted by h, then its h-dimensional Hausdorff measure vanishes but the h-dimensional...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 1997
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(97)89123-9