Conical maximal regularity for elliptic operators via Hardy spaces

Huang, Yi

doi:10.2140/apde.2017.10.1081

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Conical maximal regularity for elliptic operators via Hardy spaces

Yi Huang

Vol. 10 (2017), No. 5, 1081–1088

DOI: 10.2140/apde.2017.10.1081

Abstract

We give a technically simple approach to the maximal regularity problem in parabolic tent spaces for second-order, divergence-form, complex-valued elliptic operators. By using the associated Hardy space theory combined with certain $L^{2}$ - $L^{2}$ off-diagonal estimates, we reduce the tent space boundedness in the upper half-space to the reverse Riesz inequalities in the boundary space. This way, we also improve recent results obtained by P. Auscher et al.

Keywords

maximal regularity operators, tent spaces, elliptic operators, Hardy spaces, off-diagonal decay, maximal $L^p$-regularity

Mathematical Subject Classification 2010

Primary: 42B37

Secondary: 47D06, 42B35, 42B20

Milestones

Received: 14 April 2016

Accepted: 3 April 2017

Published: 1 July 2017

Authors

Yi Huang
Laboratoire de Mathématiques d’Orsay Université Paris-Sud Centre National de la Recherche Scientifique Université Paris-Saclay 91405 Orsay France

Vol. 10, No. 5, 2017