On Some Fourier Asymptotes of Fractal Measures

Abstract

We give a condition for a quasi-regular set to satisfy certain density, if  is absolutely continuous with respect to  and an inequality was hold. We investigate a Fourier asymptotic of fractal measures with a sharp bound. For a continuous measure with a monotone discrete sequence a best estimate was proved.

Keywords: Maximal functions, Wiener’s Measures, Fractal Measures, quasi-regular