HARDY–BLOCH TYPE SPACES AND LACUNARY SERIES ON THE POLYDISK

AVETISYAN, K. L.

Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 345-356

Résumé

We extend the well-known Paley and Paley-Kahane-Khintchine inequalities on lacunary series to the unit polydisk of . Then we apply them to obtain sharp estimates for the mean growth in weighted spaces h(p, α), h(p, log(α)) of Hardy–Bloch type, consisting of functions n-harmonic in the polydisk. These spaces are closely related to the Bloch and mixed norm spaces and naturally arise as images under some fractional operators.

Détail

DOI : 10.1017/S001708950700359X

Mots-clés : 32A37, 32A05

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