9 papers
On the Assouad dimension of Weierstrass function graphs
Efstathios Konstantinos Chrontsios Garitsis
The class of Weierstrass functions is one of the first class of examples of continuous and nowhere differentiable real functions. A challenging line of research has been…
Sobolev spaces on snowtrees
Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis
We introduce a discrete-energy Sobolev space on Ahlfors regular snowtrees, a class of metric trees where every arc is a snowflake of the same ty…
Universal quasiconformal trees
Efstathios Konstantinos Chrontsios Garitsis, Fotis Ioannidis, Vyron Vellis
A quasiconformal tree is a doubling (compact) metric tree in which the diameter of each arc is comparable to the distance of its endpoints. We show that for each integer ,…
Dimensions and metric dyadic cubes
Efstathios Konstantinos Chrontsios Garitsis
In this note, we provide equivalent definitions for fractal geometric dimensions through dyadic cube constructions. Given a metric space with finite Assouad dimension, i.e., sa…
Hölder spiral arcs
Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis
We establish a quantitative necessary and sufficient condition for a spiral arc to be a Hölder arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and…
Hölder continuity and dimensions of fractal Fourier series
Efstathios Konstantinos Chrontsios Garitsis, AJ Hildebrand
Motivated by applications in number theory, analysis, and fractal geometry, we consider regularity properties and dimensions of graphs associated with Fourier series of the form $F…