Multiparameter singular integrals and maximal operators along flat surfaces

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study double Hilbert transforms and maximal functions along surfaces of the form (t1, t2, γ1(t 12(t2)). The LP(ℝ 3) boundedness of the maximal operator is obtained if each γi is a convex increasing and γi(0) = 0. The double Hilbert transform is bounded in LP(ℝ3) if both γi's above are extended as even functions. If γ1 is odd, then we need an additional comparability condition on γ2. This result is extended to higher dimensions and the general hyper-surfaces of the form (t1,..., tn, Γ(t1,..., tn)) on ℝn+1.

Original languageEnglish
Pages (from-to)1047-1073
Number of pages27
JournalRevista Matematica Iberoamericana
Volume24
Issue number3
Publication statusPublished - 2008 Dec 1

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Hilbert Transform
Singular Integral Operator
Maximal Operator
Even function
Maximal Function
Higher Dimensions
Hypersurface
Boundedness
Odd
Form

Keywords

  • Flat surface
  • Multiple hubert transform
  • Singular radon transform

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Multiparameter singular integrals and maximal operators along flat surfaces. / Cho, Yong Kum; Hong, Sunggeum; Kim, Joonil; Yang, Chan Woo.

In: Revista Matematica Iberoamericana, Vol. 24, No. 3, 01.12.2008, p. 1047-1073.

Research output: Contribution to journalArticle

Cho, Yong Kum ; Hong, Sunggeum ; Kim, Joonil ; Yang, Chan Woo. / Multiparameter singular integrals and maximal operators along flat surfaces. In: Revista Matematica Iberoamericana. 2008 ; Vol. 24, No. 3. pp. 1047-1073.
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