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VMO Space Associated with Parabolic Sections and its Application

Published online by Cambridge University Press:  20 November 2018

Ming-Hsiu Hsu and
Ming-Yi Lee
Ming-Hsiu Hsu
Affiliation:
Department of Mathematics, National Central University, Chung-Li, 32054, Taiwan e-mail: hsumh@math.ncu.edu.tw mylee@math.ncu.edu.tw
Ming-Yi Lee
Affiliation:
Department of Mathematics, National Central University, Chung-Li, 32054, Taiwan e-mail: hsumh@math.ncu.edu.tw mylee@math.ncu.edu.tw
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Abstract

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In this paper we define a space $VM{{O}_{P}}$ associated with a family $P$ of parabolic sections and show that the dual of $VM{{O}_{P}}$ is the Hardy space $H_{P}^{1}$ . As an application, we prove that almost everywhere convergence of a bounded sequence in $H_{P}^{1}$ implies weak $^{\star }$ convergence

Keywords

42B30Monge-Ampère equationparabolic sectionHardy spaceBMOVMO

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 3 , 01 September 2015, pp. 507 - 518
Copyright
Copyright © Canadian Mathematical Society 2015

References

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