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A maximal function characterization of the Hardy space for the Gauss measure

Giancarlo Mauceri ; Stefano Meda ; Peter Sjögren (Institutionen för matematiska vetenskaper, matematik)
Proceedings of the American Mathematical Society (1088-6826). Vol. 141 (2013), 5, p. 1679-1692.
[Artikel, refereegranskad vetenskaplig]

An atomic Hardy space $ H^1(\gamma )$ associated to the Gauss measure $ \gamma $ in $ \mathbb{R}^n$ has been introduced by the first two authors. We first prove that it is equivalent to use $ (1,r)$- or $ (1,\infty )$-atoms to define this $ H^1(\gamma )$. For $ n=1$, a maximal function characterization of $ H^1(\gamma )$ is found. In arbitrary dimension, we give a description of the nonnegative functions in $ H^1(\gamma )$ and use it to prove that $ L^p(\gamma )\subset H^1(\gamma )$ for $ 1



Denna post skapades 2010-12-01. Senast ändrad 2016-11-07.
CPL Pubid: 129942

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys

Chalmers infrastruktur