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 1File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
