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HARDY–BLOCH TYPE SPACES AND LACUNARY SERIES ON THE POLYDISK

Published online by Cambridge University Press:  09 August 2007

K. L. AVETISYAN
K. L. AVETISYAN*
Affiliation:
Faculty of Physics, Yerevan State University, Alex Manoogian st. 1, Yerevan, 375025, Armenia e-mail: avetkaren@ysu.am
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Abstract

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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.

Keywords

32A3732A05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 2 , May 2007 , pp. 345 - 356
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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