Littlewood-type theorems for Hardy spaces in infinitely many variables. (English) Zbl 07863195
Summary: Littlewood’s theorem is one of the pioneering results in random analytic functions over the open unit disk. In this paper, we prove some analogues of this theorem for Hardy spaces in infinitely many variables. Our results not only cover finite-variable setting, but also apply in cases of Dirichlet series.
MSC:
| 46E50 | Spaces of differentiable or holomorphic functions on infinite-dimensional spaces |
| 30B50 | Dirichlet series, exponential series and other series in one complex variable |
| 32A35 | \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables |
Keywords:
random analytic function; Littlewood’s theorem; Hardy space; infinitely many variables; Dirichlet seriesReferences:
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