Abstract
We study double Hilbert transforms and maximal functions along surfaces of the form (t1, t2, γ1(t 1)γ2(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 language | English |
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Pages (from-to) | 1047-1073 |
Number of pages | 27 |
Journal | Revista Matematica Iberoamericana |
Volume | 24 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2008 |
Keywords
- Flat surface
- Multiple hubert transform
- Singular radon transform
ASJC Scopus subject areas
- Mathematics(all)