TY - JOUR
T1 - Group actions, the mattila integral and applications
AU - Liu, Bochen
N1 - Publisher Copyright:
©2019 Amerian Mathematial Soiety.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85061906203&partnerID=8YFLogxK
U2 - 10.1090/proc/14406
DO - 10.1090/proc/14406
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AN - SCOPUS:85061906203
SN - 0002-9939
VL - 147
SP - 2503
EP - 2516
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 6
ER -