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# VMO Space Associated with Parabolic Sections and its Application

Published:2015-03-03
Printed: Sep 2015
• Ming-Hsiu Hsu,
Department of Mathematics, National Central University, Chung-Li, 32054, Taiwan
• Ming-Yi Lee,
Department of Mathematics, National Central University, Chung-Li, 32054, Taiwan
 Format: LaTeX MathJax PDF

## Abstract

In this paper we define $VMO_\mathcal{P}$ space associated with a family $\mathcal{P}$ of parabolic sections and show that the dual of $VMO_\mathcal{P}$ is the Hardy space $H^1_\mathcal{P}$. As an application, we prove that almost everywhere convergence of a bounded sequence in $H^1_\mathcal{P}$ implies weak* convergence.
 Keywords: Monge-Ampere equation, parabolic section, Hardy space, BMO, VMO
 MSC Classifications: 42B30 - $H^p$-spaces

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