Non-homogeneous Square Functions on General Sets : Suppression and Big Pieces Methods
- Martikainen, Henri
- Mourgoglou, Mihalis
- Vuorinen, Emil
DOIAbstract
We aim to showcase the wide applicability and power of the big pieces and suppression methods in the theory of local Tb theorems. The setting is new: we consider conical square functions with cones {x is an element of R-n \ E : |x-y| <2 dist (x, E)} y is an element of E , defined on general closed subsets E subset of R-n supporting a non-homogeneous measure mu. We obtain boundedness criteria in this generality in terms of weak type testing of measures on regular balls B subset of E, which are doubling and of small boundary. Due to the general set E we use metric space methods. Therefore, we also demonstrate the recent techniques from the metric space point of view, and show that they yield the most general known local Tb theorems even with ...
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