Strichartz–Tse conjecture on integrability of harmonic energy-measure densities

Let $K$ be the Sierpiński gasket. For a nonconstant harmonic function $h$ on $K$, let $u_h=\mu_h/\mu_h(K)$ be its normalized energy measure. For nonconstant harmonic functions $h_1,h_2$ on $K$, Strichartz–Tse's conjecture.

$$\frac{d\nu_{h_1}}{d\nu_{h_2}}\in L^p(\nu_{h_2})\qquad\text{for }1<p<\frac{\log 15}{\log 9}.$$

This conjecture gives a quantitative range of $L^p$-integrability for Radon–Nikodym densities between normalized harmonic energy measures. It was proposed by Strichartz and Tse based on numerical experiments and is equivalent to uniform boundedness of the associated density-ratio power sums; the supplied source does not indicate that it has been resolved.