Maximal operators given by Fourier multipliers with dilation of fractional dimensions

2024/05/27 by Lee, Jin Bong, Seo, Jinsol
#42B15 #42B25 #42B35 #42B37 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.16855

Abstract

In this paper, we investigate L^p bounds of maximal Fourier multiplier operators with dilation of fractional dimensions. For Fourier multipliers, we suggest a criterion related to dimensions of dilation sets which guarantees L^p bounds of the maximal operators for each p. Our criterion covers Mikhlin-type multipliers, multipliers with limited decay, and multipliers with slow decay.

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