Conical maximal regularity for elliptic operators via Hardy spaces

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.