Multiparameter singular integrals and maximal operators along flat surfaces

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

Research output: Contribution to journalArticlepeer-review

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
DOIs
Publication statusPublished - 2008

Keywords

  • Flat surface
  • Multiple hubert transform
  • Singular radon transform

ASJC Scopus subject areas

  • Mathematics(all)

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