= Inhomogeneous oscillation decay implies Hölder continuity
{title2=$\omega(R/2)\leq\theta\omega(R)+AR^\alpha$}
If the essential oscillation on concentric balls obeys $\omega(R/2)\leq\theta\omega(R)+AR^\alpha$ with $0<\theta<1$ and $\alpha>0$, dyadic iteration gives $\omega(r)\leq Cr^\mu$ for every $0<\mu<\min\{\alpha,-\log_2\theta\}$. The resulting decay gives a <Hölder continuous function>. Taking the exponent strictly below both decay rates avoids a logarithmic factor when the rates coincide.
Back to article page
