Regularity and modulus of continuity of space-filling curves

Abstract

We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example.

Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees

“…Dyadic energy has also been used to study the regularity and modulus of continuity of space-filling curves. One of the motivations for this paper is the approach in [20]. Given a continuous g : S 1 → R n , consider the dyadic energy (1.1) E(g; p, λ) :=…”