Vol. 10, No. 5, 2017

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Conical maximal regularity for elliptic operators via Hardy spaces

Yi Huang

Vol. 10 (2017), No. 5, 1081–1088

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 L2-L2 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.

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
Received: 14 April 2016
Accepted: 3 April 2017
Published: 1 July 2017
Yi Huang
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud
Centre National de la Recherche Scientifique
Université Paris-Saclay
91405 Orsay