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Discrete bilinear Radon transforms along arithmetic functions with many common values
Author(s) -
Dong Dong,
Meng Xianchang
Publication year - 2018
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12127
Subject(s) - mathematics , euler's totient function , prime (order theory) , bilinear interpolation , bounded function , function (biology) , discrete mathematics , combinatorics , pure mathematics , euler's formula , arithmetic , mathematical analysis , statistics , evolutionary biology , biology
We prove that for a large class of functions P and Q , there exists d ∈ ( 0 , 1 ) such that the discrete bilinear Radon transformB P , Q dis( f , g ) ( n ) = ∑ m ∈ Z ∖ { 0 } f ( n − P ( m ) ) g ( n − Q ( m ) ) 1 mis bounded froml 2 × l 2into l 1 + εfor any ε ∈ ( d , 1 ) . In particular, the boundedness holds for any ε ∈ ( 0 , 1 ) when P (or Q ) is the Euler totient function ϕ ( | m | ) or the prime counting function π ( | m | ) .