Group actions, the mattila integral and applications

Bochen Liu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The Mattila integral, (Formula Presented) developed by Mattila, is the main tool in the study of the Falconer distance conjecture. In this paper we develop a generalized version of the Mattila integral that worKs on more general Falconer-type problems. As applications, we consider when the product of distance set(Formula Presented) has positive Lebesgue measure and when the sum-product set E · (F + H) = {x · (y + z): x ∈ E ⊂ R2, y ∈ F ⊂ R2, z ∈ H ⊂ R2 }, has positive Lebesgue.

Original languageEnglish
Pages (from-to)2503-2516
Number of pages14
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - 2019

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©2019 Amerian Mathematial Soiety.


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