FOURIER TRANSFORMATION AND SINGULAR INTEGRALS ON SELF-SIMILAR MEASURE

摘要

This paper serves two purposes. One is to modify Strichartz’s results with respect to theasymptotic averages of the Fourier transform of μ on , self-similar measure defined byHutchinson. Another purpose is to consider a singular integral operator on μ and show that this op-erator is of type (p,p)(1p∞).