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

Funding

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.

Keywords

11N05 (primary)
11N64
42B20

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/blms.12127

Cite this

@article{324fc84540784c5fbfc77223cd13ffc8,

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",

year = "2018",

month = feb,

day = "1",

doi = "10.1112/blms.12127",

language = "English (US)",

volume = "50",

pages = "132--142",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - Discrete bilinear Radon transforms along arithmetic functions with many common values

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

UR - https://www.scopus.com/pages/publications/85036538604

UR - https://www.scopus.com/inward/citedby.url?scp=85036538604&partnerID=8YFLogxK

U2 - 10.1112/blms.12127

DO - 10.1112/blms.12127

M3 - Article

AN - SCOPUS:85036538604

SN - 0024-6093

VL - 50

SP - 132

EP - 142

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 1

ER -

Discrete bilinear Radon transforms along arithmetic functions with many common values

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this