Lp-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets - Hofmann, Steve, 1958-; Mitrea, Dorina, 1965-; Mitrea, Marius; Morris, Andrew J. (Andrew Jordan) (Memoirs of the American Mathematical Society ;, 2017)
The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local T(b) theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local T(b) 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 ho.