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

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 $L^p$-integrable for $1 < p < \log 15 / \log 9$. That range is confirmed: the associated quantities are uniformly bounded for arbitrary ordered pairs of nonconstant harmonic functions.

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analysisJul 24, 2026Significance 10/100Registry: unreviewed

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

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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 $L^p$-integrable for $1 < p < \log 15 / \log 9$. That range is confirmed: the associated quantities are uniformly bounded for arbitrary ordered pairs of nonconstant harmonic functions.

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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 $L^p$-integrable for $1 < p < \log 15 / \log 9$. That range is confirmed: the associated quantities are uniformly bounded for arbitrary ordered pairs of nonconstant harmonic functions.

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