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๐ฟ^{๐‘}-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets

๐ฟ^{๐‘}-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets

We 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, we consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient โ€ฆ