A value-distribution criterion for the class $L\log L$ and some related questions

Essen, M.; Shea, D. F.; Stanton, C. S.

Annales de l'Institut Fourier, Tome 35 (1985) no. 4, pp. 127-150

We give a necessary and sufficient condition for an analytic function in $H^1$ to have real part in class $L$ $logL$. This condition contains the classical one of Zygmund; other variants are also given.

Nous donnons une condition nécessaire et suffisante pour qu’une fonction analytique dans $H^1$ ait une partie réelle dans la classe $L$ $logL$. Cette condition généralise la condition classique de Zygmund ; on donne aussi d’autres conditions suffisantes.

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