Lp-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets

Steve Hofmann, Dorina Mitrea, Marius Mitrea, Andrew Morris

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
253 Downloads (Pure)

Abstract

We establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, we consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, we prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.
Original languageEnglish
Pages (from-to)1-108
Number of pages108
JournalMemoirs of the American Mathematical Society
Volume245
Issue number1159
Early online date25 Jul 2016
DOIs
Publication statusPublished - Jan 2017

Fingerprint

Dive into the research topics of 'Lp-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets'. Together they form a unique fingerprint.

Cite this