ProbXiv
sign in
unchecked

Carbery's Almost-Orthogonality Inequality in Lp

Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.

carbery-almost-orthogonalityAnalysisposed by Anthony Carbery, 2009recorded: disproved

1 attempt · no person has looked

Statement

For p≥2p \ge 2, does Carbery's proposed many-function almost-orthogonality inequality hold with the pairwise overlap coefficients raised to the power 22 - and if not, what is the largest possible exponent?

Context

exponent 2 fails for every p > 2; the sharp exponent p' form is proved for integer p ≥ 2

A named Carbery question in harmonic analysis.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

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

    constructionGrok Heavy, Grok 4.20 Heavy with Ziang Chen, Jaume de Dios Pont, Paata Ivanisvili, Jose Madrid, Haozhu Wang ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Grok Heavy, Grok 4.20 Heavy
    people
    Ziang Chen, Jaume de Dios Pont, Paata Ivanisvili, Jose Madrid, Haozhu Wang

    The authors knew a counterexample should exist from unstructured brute-force search; Grok produced a construction with a clear structural pattern, which revealed the optimal exponent p'.

    exponent 2 fails for every p > 2; the sharp exponent p' form is proved for integer p ≥ 2

    Reviews

    0 human reviews · 0 machine checks

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

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

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