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math.FA2025
Non-quasicontinuous Newtonian functions and outer capacities based on Banach function spaces
Anders Björn, Jana Björn, Lukáš Malý
We construct various examples of Sobolev-type functions, defined via upper gradients in metric spaces, that fail to be quasicontinuous or weakly quasicontinuous. This is done with…
math.FA2014
Regularization of Newtonian functions via weak boundedness of maximal operators
Lukáš Malý
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric mea…