Triple Hilbert transforms along polynomial surfaces

Yong Kum Cho, Sunggeum Hong, Joonil Kim, Chan Woo Yang

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

Given Ω ⊂ ℤ+ 3, we discuss a necessary and sufficient condition that the triple Hilbert transform associated with any polynomial of the form (t1,t2,t3, ∑m Ie{cyrillic, ukrainian} Ωam tm is bounded in Lp(ℝ4).

Original languageEnglish
Pages (from-to)485-528
Number of pages44
JournalIntegral Equations and Operator Theory
Volume65
Issue number4
DOIs
Publication statusPublished - 2009 Dec 1

Fingerprint

Hilbert Transform
Necessary Conditions
Polynomial
Sufficient Conditions
Form

Keywords

  • Even in column
  • Littlewood-Paley operator
  • Newton polyhedron
  • Oscillatory singular integral
  • Triple Hilbert transform
  • Van der Corput's lemma

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Triple Hilbert transforms along polynomial surfaces. / Cho, Yong Kum; Hong, Sunggeum; Kim, Joonil; Yang, Chan Woo.

In: Integral Equations and Operator Theory, Vol. 65, No. 4, 01.12.2009, p. 485-528.

Research output: Contribution to journal › Article

Cho, YK, Hong, S, Kim, J & Yang, CW 2009, 'Triple Hilbert transforms along polynomial surfaces', Integral Equations and Operator Theory, vol. 65, no. 4, pp. 485-528. https://doi.org/10.1007/s00020-009-1731-9
Cho YK, Hong S, Kim J, Yang CW. Triple Hilbert transforms along polynomial surfaces. Integral Equations and Operator Theory. 2009 Dec 1;65(4):485-528. https://doi.org/10.1007/s00020-009-1731-9
Cho, Yong Kum ; Hong, Sunggeum ; Kim, Joonil ; Yang, Chan Woo. / Triple Hilbert transforms along polynomial surfaces. In: Integral Equations and Operator Theory. 2009 ; Vol. 65, No. 4. pp. 485-528.
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