Discrete bilinear Radon transforms along arithmetic functions with many common values

Dong Dong; Xianchang Meng

doi:10.1112/blms.12127

Discrete bilinear Radon transforms along arithmetic functions with many common values

Dong Dong, Xianchang Meng

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove that for a large class of functions P and Q, there exists d ∈ (0, 1) such that the discrete bilinear Radon transform (Formula presented.) is bounded from l² × l² into l^1+E for any ∈ ∈ (d, 1). In particular, the boundedness holds for any ∈ ∈ (d, 1) when (Formula presented.) P (or Q) is the Euler totient function φ(|m|) or the prime counting function π(|m|).

Original language	English (US)
Pages (from-to)	132-142
Number of pages	11
Journal	Bulletin of the London Mathematical Society
Volume	50
Issue number	1
DOIs	https://doi.org/10.1112/blms.12127
State	Published - Feb 1 2018

Keywords

11N05 (primary)
11N64
42B20

ASJC Scopus subject areas

General Mathematics

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10.1112/blms.12127

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title = "Discrete bilinear Radon transforms along arithmetic functions with many common values",

abstract = "We prove that for a large class of functions P and Q, there exists d ∈ (0, 1) such that the discrete bilinear Radon transform (Formula presented.) is bounded from l2 × l2 into l1+E for any ∈ ∈ (d, 1). In particular, the boundedness holds for any ∈ ∈ (d, 1) when (Formula presented.) P (or Q) is the Euler totient function φ(|m|) or the prime counting function π(|m|).",

keywords = "11N05 (primary), 11N64, 42B20",

author = "Dong Dong and Xianchang Meng",

note = "Funding Information: Received 22 April 2017; revised 29 September 2017; published online 1 December 2017. 2010 Mathematics Subject Classification 42B20, 11N64, 11N05 (primary). The second author was partially supported by NSF grant DMS-1501982. Publisher Copyright: {\textcopyright} 2017 London Mathematical Society",

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AU - Dong, Dong

AU - Meng, Xianchang

N1 - Funding Information: Received 22 April 2017; revised 29 September 2017; published online 1 December 2017. 2010 Mathematics Subject Classification 42B20, 11N64, 11N05 (primary). The second author was partially supported by NSF grant DMS-1501982. Publisher Copyright: © 2017 London Mathematical Society

PY - 2018/2/1

Y1 - 2018/2/1

N2 - We prove that for a large class of functions P and Q, there exists d ∈ (0, 1) such that the discrete bilinear Radon transform (Formula presented.) is bounded from l2 × l2 into l1+E for any ∈ ∈ (d, 1). In particular, the boundedness holds for any ∈ ∈ (d, 1) when (Formula presented.) P (or Q) is the Euler totient function φ(|m|) or the prime counting function π(|m|).

AB - We prove that for a large class of functions P and Q, there exists d ∈ (0, 1) such that the discrete bilinear Radon transform (Formula presented.) is bounded from l2 × l2 into l1+E for any ∈ ∈ (d, 1). In particular, the boundedness holds for any ∈ ∈ (d, 1) when (Formula presented.) P (or Q) is the Euler totient function φ(|m|) or the prime counting function π(|m|).

KW - 11N05 (primary)

KW - 11N64

KW - 42B20

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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Discrete bilinear Radon transforms along arithmetic functions with many common values

Abstract

Keywords

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