This paper studies Newtonian Sobolev-Lorentz spaces. We prove that these spaces are Banach. We also study the global p, q-capacity and the p, q-modulus of families of rectifiable curves. Under some additional assumptions (that is, X carries a doubling measure and a weak Poincaré inequality), we show that when 1 ≤ q < p the Lipschitz functions are dense in those spaces; moreover, in the same setting we show that the p, q-capacity is Choquet provided that q > 1. We also provide a counterexample to the density result in the Euclidean setting when 1<p≤ n and q =∞. © 2013 University of Illinois.

NEWTONIAN LORENTZ METRIC SPACES

MIRANDA, Michele
2012

Abstract

This paper studies Newtonian Sobolev-Lorentz spaces. We prove that these spaces are Banach. We also study the global p, q-capacity and the p, q-modulus of families of rectifiable curves. Under some additional assumptions (that is, X carries a doubling measure and a weak Poincaré inequality), we show that when 1 ≤ q < p the Lipschitz functions are dense in those spaces; moreover, in the same setting we show that the p, q-capacity is Choquet provided that q > 1. We also provide a counterexample to the density result in the Euclidean setting when 1
2012
S., Costea; Miranda, Michele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1912014
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