Non-homogeneous Square Functions on General Sets : Suppression and Big Pieces Methods

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Martikainen , H , Mourgoglou , M & Vuorinen , E 2017 , ' Non-homogeneous Square Functions on General Sets : Suppression and Big Pieces Methods ' , Journal of Geometric Analysis , vol. 27 , no. 4 , pp. 3176-3227 . https://doi.org/10.1007/s12220-017-9801-8

Title: Non-homogeneous Square Functions on General Sets : Suppression and Big Pieces Methods
Author: Martikainen, Henri; Mourgoglou, Mihalis; Vuorinen, Emil
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2017-10
Language: eng
Number of pages: 52
Belongs to series: Journal of Geometric Analysis
ISSN: 1050-6926
URI: http://hdl.handle.net/10138/313038
Abstract: 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 assumptions formulated using balls rather than the abstract dyadic metric cubes.
Subject: Big pieces
Local Tb theorems
Good lambda method
Conical square functions
LOCAL TB THEOREM
SPACES
111 Mathematics
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