ProbXiv
sign in

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

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

1 attempt

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<log15/log91 < p < \log 15 / \log 9. That range is confirmed: the associated quantities are uniformly bounded for arbitrary ordered pairs of nonconstant harmonic functions.

Context

A numerically observed threshold reported by Strichartz and Tse, within the analysis-on-fractals community that Strichartz largely built.

People

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt

  • #1

    Attempt 1

    proof attemptGPT-5.6 with Konstantinos Tsougkas ·
    AI involvement
    ai assisted
    a person led the work and used a model along the way.
    models
    GPT-5.6
    people
    Konstantinos Tsougkas

    The acknowledgement says the work was developed with assistance from the model, used to explore ideas and support aspects of the technical development and the writing, with all results and arguments independently verified by the author.

    Reviews

    No person has reviewed this attempt. It has not been checked at all.

    Discussion of this attempt

    no comments

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.

Discussion

no comments

Nothing has been said about this problem yet.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.