Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces

2003/06/30 by Isroil A. Ikromov, I. A. Ikromov, Michael Kempe +6
Mathematics · #42B10 #42B25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #math.CA #msc:42B10 #msc:42B25

paper · pdf · doi:10.48550/arxiv.math/0306429

16 pages

arxiv created 2003/06/30 · openalex publication_date 2003/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundedness problem for maximal operators in 3-dimensional Euclidean space associated to hypersurfaces given as the graph of c+f, where f is a mixed homogeneous function which is smooth away from the origin and c is a constant. Our result generalizes a corresponding theorem on mixed homogeneous polynomial functions by A. Iosevich and E. Sawyer.

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