Maximal operators given by Fourier multipliers with dilation of fractional dimensions
Abstract
In this paper, we investigate Lp 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 Lp 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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