Geodesic
Random Dirichlet Functions: Multipliers and Smoothness
Canadian journal of mathematics, Tome 45 (1993) no. 2, pp. 255-268

Voir la notice de l'article provenant de la source Cambridge University Press

We show that if is a holomorphic function in the Dirichlet space of the unit disk, then almost all of its randomizations are multipliers of that space. This parallels a known result for lacunary power series, which also has a version for smoothness classes: every lacunary Dirichlet series lies in the Lipschitz class Lip1/2 of functions obeying a Lipschitz condition with exponent 1/2. However, unlike the lacunary situation, no corresponding “almost sure” Lipschitz result is possible for random series: we exhibit a Dirichlet function with norandomization in Lip1/2. We complement this result with a “best possible” sufficient condition for randomizations to belong almost surely to Lip1/2. Versions of our results hold for weighted Dirichlet spaces, and much of our work is carried out in this more general setting.
DOI : 10.4153/CJM-1993-012-6
Mots-clés : 30B20, 47B38 
Cochran, W. George; Shapiro, Joel H.; Ullrich, David C. Random Dirichlet Functions: Multipliers and Smoothness. Canadian journal of mathematics, Tome 45 (1993) no. 2, pp. 255-268. doi: 10.4153/CJM-1993-012-6
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