Sökning: id:"swepub:oai:lup.lub.lu.se:1d4e6a02-9afd-47b0-953e-1f7f7ab23e4c" >
Fatou and brothers ...
Fatou and brothers Riesz theorems in the infinite-dimensional polydisc
-
- Aleman, Alexandru (författare)
- Lund 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
-
- Olsen, Jan Fredrik (författare)
- Lund 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
-
- Saksman, Eero (författare)
- University of Helsinki
-
(creator_code:org_t)
- 2019-04-10
- 2019
- Engelska.
-
Ingår i: Journal d'Analyse Mathematique. - : Springer Science and Business Media LLC. - 0021-7670 .- 1565-8538. ; 137:1, s. 429-447
- Relaterad länk:
-
http://dx.doi.org/10...
-
visa fler...
-
https://helda.helsin...
-
https://lup.lub.lu.s...
-
https://doi.org/10.1...
-
visa färre...
Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
Hitta via bibliotek
Till lärosätets databas