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.

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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