Almost-orthogonality principles for certain directional maximal functions

2020/03/31 by Kim, Jongchon
#42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.00141

Abstract

We develop almost-orthogonality principles for maximal functions associated with averages over line segments and directional singular integrals. Using them, we obtain sharp L²-bounds for these maximal functions when the underlying direction set is equidistributed in \mathbbS^n-1.

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