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Hardy-Bloch type spaces and lacunary series on the polydisk. (English) Zbl 1123.32004
Summary: We extend the well-known Paley and Paley-Kahane-Khintchine inequalities on lacunary series to the unit polydisk of \(\mathbb C^n\). Then we apply them to obtain sharp estimates for the mean growth in weighted spaces \(h(p,\alpha), h(p, \log(\alpha))\) 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.

32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
32A05 Power series, series of functions of several complex variables
Full Text: DOI
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