On Convolution Squares of Singular Measures

convolution square;singular measure;Lipschitz;Hausdorff dimension;Pure Mathematics

Chan, Vincent

University of Waterloo

关键词: convolution square;    singular measure;    Lipschitz;    Hausdorff dimension;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5369/1/thesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

We prove that if $1 > alpha > 1/2$, then there exists a probability measure $mu$ such that the Hausdorff dimension of its support is $alpha$ and $mu*mu$ is a Lipschitz function of class $alpha-1/2$.