= Log-Lipschitz modulus
{title2=$\mu(r)=r(1-\log r)\quad(0<r\leq1)$}
Set $\mu(0)=0$ and extend $\mu(r)=1$ for $r\geq1$. This positive, nondecreasing <modulus of continuity> is weaker than a linear <Lipschitz continuity> bound but still has $\int_0^1dr/\mu(r)=\infty$. At small distances it is equivalent to $r\log(1/r)$. A signed $r\log r$ cannot be an upper modulus at distances less than one. The <planar vorticity velocity kernel> maps $L^1\cap L^\infty$ into velocity fields with this modulus.
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