Square Function and Heat Flow Estimates on Domains


The first purpose of this note is to provide a proof of the usual square function estimate on L(Ω). It turns out to follow directly from a generic Mikhlin multiplier theorem obtained by Alexopoulos, which mostly relies on Gaussian bounds on the heat kernel. We also provide a simple proof of a weaker version of the square function estimate, which is enough in most instances involving dispersive PDEs. Moreover, we obtain, by a relatively simple integration by parts, several useful L(Ω;H) bounds for the derivatives of the heat flow with values in a given Hilbert space H.

Cite this paper

@inproceedings{Ivanovici2009SquareFA, title={Square Function and Heat Flow Estimates on Domains}, author={Oana Ivanovici and Frederic Planchon}, year={2009} }