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
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