A geometric proof of Bourgain's L² estimate of maximal operators along analytic vector fields

2015/06/29 by Shaoming Guo, Guo, Shaoming
Mathematics · #42B20 #42B25 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #math.CA #msc:42B20 #msc:42B25

paper · pdf · doi:10.48550/arxiv.1506.08633

15 pages

openalex publication_date 2015/06/29 · arxiv created 2015/07/20 · arxiv updated 2015/07/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Bourgain proved that the maximal operator associated to an analytic vector field is bounded on L². In the present paper, we give a geometric proof of Bourgain's result by using the tools developed by Lacey and Li.

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