A poor man's square function estimate on domains

Oana Ivanovici (1) , Fabrice Planchon (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LAGA - Laboratoire Analyse, Géométrie et Applications

The purpose of this note is to provide an elementary proof of a weak version of the square function estimate on L^p(Omega) which is often used in the context of wave or Schrodinger equations to reduce estimates for data in Sobolev spaces to spectrally localized data. In the process we obtain usefull L^p(Omega) bounds for the heat kernel and its derivatives, through a simple argument which holds irrespective of the domain.

Domaines: Equations aux dérivées partielles [math.AP]

Oana Ivanovici, Fabrice Planchon. A poor man's square function estimate on domains. 2008. ⟨hal-00347161v2⟩