Asian Journal of Mathematics

Volume 20 (2016)

Number 1

Characterization of Campanato spaces associated with parabolic sections

Pages: 183 – 198

DOI: https://dx.doi.org/10.4310/AJM.2016.v20.n1.a8

Authors

Ming-Yi Lee (Department of Mathematics, National Central University, Taiwan)

Chin-Cheng Lin (Department of Mathematics, National Central University, Taiwan)

Xinfeng Wu (Department of Mathematics, China University of Mining & Technology, Beijing, China)

Abstract

We study the Campanato spaces $\Lambda^{\kappa}_{q, \mathcal{P}}$ associated with a family $\mathcal{P}$ of parabolic sections which are closely related to the parabolic Monge–Ampère equation. We characterize these spaces in terms of Lipschitz spaces $\mathrm{Lip}^{\alpha}_{\mathcal{P}}$. We also introduce the corresponding Hardy spaces $H^{p}_{\mathcal{P}}$ and demonstrate the equivalence between the Littlewood-Paley $g$-functions and atomic decompositions for elements in $H^{p}_{\mathcal{P}}$. Moreover, we show that Campanato spaces are the duals of Hardy spaces.

Keywords

Campanato spaces, Hardy spaces, Lipschitz spaces, Monge–Ampère equations, parabolic sections

2010 Mathematics Subject Classification

42B30, 42B35

Published 28 January 2016