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.

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: 10.24033/bsmf.2562
Classification: 42A16
Keywords: convolution square, self convolution, singular measure
Mot clés : convolution carr'ee, mesure singuliére
@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},
     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/}
}
TY  - JOUR
AU  - Körner, Thomas
TI  - On a theorem of Saeki concerning convolution squares of singular measures
JO  - Bulletin de la Société Mathématique de France
PY  - 2008
SP  - 439
EP  - 464
VL  - 136
IS  - 3
PB  - Société mathématique de France
UR  - http://www.numdam.org/articles/10.24033/bsmf.2562/
DO  - 10.24033/bsmf.2562
LA  - en
ID  - BSMF_2008__136_3_439_0
ER  - 
%0 Journal Article
%A Körner, Thomas
%T On a theorem of Saeki concerning convolution squares of singular measures
%J Bulletin de la Société Mathématique de France
%D 2008
%P 439-464
%V 136
%N 3
%I Société mathématique de France
%U http://www.numdam.org/articles/10.24033/bsmf.2562/
%R 10.24033/bsmf.2562
%G en
%F 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/articles/10.24033/bsmf.2562/

[1] N. K. Bary - A treatise on trigonometric series. Vols. I, II, Authorized translation by Margaret F. Mullins. A Pergamon Press Book, The Macmillan Co., 1964. | MR | Zbl

[2] C. C. Graham & O. C. Mcgehee - Essays in commutative harmonic analysis, Grund. Math. Wiss., vol. 238, Springer, 1979. | MR | Zbl

[3] G. R. Grimmett & D. R. Stirzaker - Probability and random processes, third éd., Oxford University Press, 2001. | MR | Zbl

[4] S. K. Gupta & K. E. Hare - « On convolution squares of singular measures », Colloq. Math. 100 (2004), p. 9-16. | MR | Zbl

[5] F. Hausdorff - Set theory, Chelsea Publishing Company, New York, 1957. | MR | Zbl

[6] W. Hoeffding - « Probability inequalities for sums of bounded random variables », J. Amer. Statist. Assoc. 58 (1963), p. 13-30. | MR | Zbl

[7] J.-P. Kahane & R. Salem - Ensembles parfaits et séries trigonométriques, Actualités Sci. Indust., No. 1301, Hermann, 1963. | MR | Zbl

[8] R. Kaufman - « Small subsets of finite abelian groups », Ann. Inst. Fourier (Grenoble) 18 (1968), p. 99-102 V. | Numdam | MR | Zbl

[9] K. Kuratowski - Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, 1966. | MR | Zbl

[10] S. Saeki - « On convolution squares of singular measures », Illinois J. Math. 24 (1980), p. 225-232. | MR | Zbl

[11] N. Wiener & A. Wintner - « Fourier-Stieltjes Transforms and Singular Infinite Convolutions », Amer. J. Math. 60 (1938), p. 513-522. | JFM | MR

Cited by Sources: