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Fatou and brothers ...
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Aleman, AlexandruLund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
(författare)
Fatou and brothers Riesz theorems in the infinite-dimensional polydisc
- Artikel/kapitelEngelska2019
Förlag, utgivningsår, omfång ...
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2019-04-10
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Springer Science and Business Media LLC,2019
Nummerbeteckningar
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LIBRIS-ID:oai:lup.lub.lu.se:1d4e6a02-9afd-47b0-953e-1f7f7ab23e4c
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https://lup.lub.lu.se/record/1d4e6a02-9afd-47b0-953e-1f7f7ab23e4cURI
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https://doi.org/10.1007/s11854-019-0006-xDOI
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Språk:engelska
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Sammanfattning på:engelska
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Ämneskategori:art swepub-publicationtype
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We study the boundary behavior of functions in the Hardy spaces on the infinite-dimensional polydisc. These spaces are intimately related to the Hardy spaces of Dirichlet series. We exhibit several Fatou and Marcinkiewicz- Zygmund type theorems for radial convergence of functions with Fourier spectrum supported on N0∞∪(−N0∞). As a consequence one obtains easy new proofs of the brothers F. and M. Riesz Theorems in infinite dimensions, as well as being able to extend a result of Rudin concerning which functions are equal to the modulus of an H 1 function almost everywhere to T ∞ . Finally, we provide counterexamples showing that the pointwise Fatou theorem is not true in infinite dimensions without restrictions to the mode of radial convergence even for bounded analytic functions.
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Olsen, Jan FredrikLund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)math-jon
(författare)
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Saksman, EeroUniversity of Helsinki(Swepub:lu)math-esa
(författare)
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Matematik (naturvetenskapliga fakulteten)Matematikcentrum
(creator_code:org_t)
Sammanhörande titlar
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Ingår i:Journal d'Analyse Mathematique: Springer Science and Business Media LLC137:1, s. 429-4470021-76701565-8538
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