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Strichartz-Tse L^p-Integrability on the Sierpinski Gasket

Analysis · posed by Robert S. Strichartz, Samuel Tse · solved

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Statement

Energy measures of any two nonconstant harmonic functions on the standard Sierpinski gasket are mutually absolutely continuous. Strichartz and Tse reported numerical evidence that the Radon-Nikodym densities are LpL^p-integrable for 1<p<log⁡15/log⁡91 < p < \log 15 / \log 9. That range is confirmed: the associated quantities are uniformly bounded for arbitrary ordered pairs of nonconstant harmonic functions.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Konstantinos Tsougkas, using GPT-5.6

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