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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
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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 Monge-Ampere equation, parabolic section, Hardy space, BMO, VMO
MSC Classifications: 42B30 show english descriptions $H^p$-spaces 42B30 - $H^p$-spaces
 

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