SPD

Abstract

Square function norms, as in the Burkholder-Davis-Gundy inequalities for vector-valued martingales, also play an important role in harmonic analysis and spectral theory, e.g. in the Paley-Littlewood theory for elliptic operators. Methods from these three theories intersect in existence and regularity theorems for SPDE and it is therefore natural to explore how the regularity of their solutions can be expressed in these norms. In particular one can prove maximal regularity results for equations in reflexive L_p spaces, which directly extend the known Hilbert space results. For p strictly between 1 and 2, these are the first maximal regularity results in the literature.