convergence almost everywhere
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2018 ◽  
Vol 7 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Hoai-Minh Nguyen ◽  
Andrea Pinamonti ◽  
Marco Squassina ◽  
Eugenio Vecchi

AbstractWe establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in terms of nonlocal functionals. The first one is related to the BBM formula, due to Bourgain, Brezis and Mironescu. The second one is related to the work of the first author on the classical Sobolev spaces. We also study the convergence almost everywhere and the convergence in {L^{1}} appearing naturally in these contexts.



2017 ◽  
Vol 370 (3) ◽  
pp. 1629-1659
Author(s):  
Mieczysław Mastyło ◽  
Luis Rodríguez-Piazza






2015 ◽  
Vol 353 (10) ◽  
pp. 883-886 ◽  
Author(s):  
Michel J.G. Weber


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