On a theorem of Saeki concerning convolution squares of singular measures

Körner, Thomas

doi:10.24033/bsmf.2562

On a theorem of Saeki concerning convolution squares of singular measures
[Carrés de convolution des mesures singulières]

Körner, Thomas

Bulletin de la Société Mathématique de France, Tome 136 (2008) no. 3, pp. 439-464.

Résumé
Abstract

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 $α - \frac{1}{2}$ .

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 $α - \frac{1}{2}$ .

MR Zbl

DOI : 10.24033/bsmf.2562

Classification : 42A16
Keywords: convolution square, self convolution, singular measure
Mot clés : convolution carr'ee, mesure singuliére

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     title = {On a theorem of {Saeki} concerning convolution squares of singular measures},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {439--464},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {136},
     number = {3},
     year = {2008},
     doi = {10.24033/bsmf.2562},
     mrnumber = {2415349},
     zbl = {1183.42004},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2562/}
}

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Körner, Thomas. On a theorem of Saeki concerning convolution squares of singular measures. Bulletin de la Société Mathématique de France, Tome 136 (2008) no. 3, pp. 439-464. doi : 10.24033/bsmf.2562. http://www.numdam.org/articles/10.24033/bsmf.2562/

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