A Discrete Quadratic Carleson Theorem on with ℓ2 a Restricted Supremum. (24th June 2016)
- Record Type:
- Journal Article
- Title:
- A Discrete Quadratic Carleson Theorem on with ℓ2 a Restricted Supremum. (24th June 2016)
- Main Title:
- A Discrete Quadratic Carleson Theorem on with ℓ2 a Restricted Supremum
- Authors:
- Krause, Ben
Lacey, Michael T. - Abstract:
- Abstract : Consider the discrete maximal function acting on ℓ 2 ( ℤ ) functions C Λ f ( n ) : = sup λ ∈ Λ | ∑ m ≠ 0 f ( n − m ) e 2 π i λ m 2 m, | where Λ ⊂ [ 0, 1 ] . We give sufficient conditions on Λ, met by certain kinds of Cantor sets, for this to be a bounded sublinear operator. This result is a discrete analogue of E.M.Stein's integral result, that the maximal operator below is bounded on L 2 ( ℝ ) . C 2 f ( x ) : = sup λ ∈ ℝ | ∫ f ( x − y ) e 2 π i λ y 2 y d y | . The proof of our result relies heavily on Bourgain's work on arithmetic ergodic theorems, with novel complexity arising from the oscillatory nature of the question at hand, and difficulties arising from the parameter λ above.
- Is Part Of:
- International mathematics research notices. Volume 2017:Number 10(2017)
- Journal:
- International mathematics research notices
- Issue:
- Volume 2017:Number 10(2017)
- Issue Display:
- Volume 2017, Issue 10 (2017)
- Year:
- 2017
- Volume:
- 2017
- Issue:
- 10
- Issue Sort Value:
- 2017-2017-0010-0000
- Page Start:
- 3180
- Page End:
- 3208
- Publication Date:
- 2016-06-24
- Subjects:
- Mathematics -- Periodicals
510 - Journal URLs:
- http://imrn.oxfordjournals.org/ ↗
http://ukcatalogue.oup.com/ ↗ - DOI:
- 10.1093/imrn/rnw116 ↗
- Languages:
- English
- ISSNs:
- 1073-7928
- Deposit Type:
- Legaldeposit
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 4544.001000
British Library DSC - BLDSS-3PM
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- 26701.xml