Convolution estimates for measures on some complex curves

2015/03/30 by Hyunuk Chung, Chung, Hyunuk, Seheon Ham +1
Mathematics · #42B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42B10

paper · pdf · doi:10.48550/arxiv.1503.08569

39 pages

arxiv created 2015/03/30 · arxiv updated 2015/03/31

Abstract

We consider the convolution operator for a measure supported on complex curves. The measure which we consider here is an analogue of the affine arclength measure for real curves. By modifying a combinatorial argument called the band structure argument, we prove the (nearly) optimal Lorentz space estimates. This includes the optimal strong type estimates as special cases. The complex curves we consider here are the ones considered for the Fourier restriction estimates for complex curves in \citeBH.

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