On a theorem of Saeki concerning convolution squares of singular measures
Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 3, p. 439-464

If 1>α>1/2, then there exists a probability measure μ such that the Hausdorff dimension of the support of μ is α and μ*μ is a Lipschitz function of class α-1 2.

Si 1>α>1/2, alors il existe une mesure de probabilité μ avec support de dimension d’Hausdorff α tel que μ*μ est une fonction Lipschitz de classe α-1 2.

DOI : https://doi.org/10.24033/bsmf.2562
Classification:  42A16
Keywords: convolution square, self convolution, singular measure
@article{BSMF_2008__136_3_439_0,
     author = {K\"orner, Thomas},
     title = {On a theorem of Saeki concerning convolution squares of singular measures},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {136},
     number = {3},
     year = {2008},
     pages = {439-464},
     doi = {10.24033/bsmf.2562},
     zbl = {1183.42004},
     mrnumber = {2415349},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2008__136_3_439_0}
}
Körner, Thomas. On a theorem of Saeki concerning convolution squares of singular measures. Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 3, pp. 439-464. doi : 10.24033/bsmf.2562. http://www.numdam.org/item/BSMF_2008__136_3_439_0/

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