# HARMONIC DOUBLING CONDITION AND JOHN DISKS

• Kim, Ki-Won (Department of Mathematics, Pusan Womens University)
• Published : 1995.01.01

#### Abstract

A Jordan domain D in C is said to be a c-quasidisk if there exists a constant $c \geq 1$ such that each two points $z_1$ and $z_2$ in D can be joined by an arc $\tau$ in D such that $$\ell(\tau) \leq c\midz_1 - z_2\mid$$ and $$(1.1) min(\ell(\tau_1),\ell(\tau_2)) \leq c d(z, \partial D)$$ for all $z \in \tau$, where $\tau_1$ and $\tau_2$ are the components of $\tau\{z}$. Quasidisks have been extensively studied and can be characterized in many different ways [1],[2],[3].