Sobolev y Besov en espacios métricos

HARBOURE, ELEONOR OFELIA; AIMAR, HUGO ALEJANDRO; MARCOS, MIGUEL ANDRÉS

Mar del Plata

Encuentro; XI Encuentro Nacional de Analistas A. P. Calderón; 2012

An extension of Sobolev spaces W^1,p for metric spaces with 'enough' paths is presented in [Sh]; Several classical results from W^1,p still work on N^1,p; In R^n, Besov spaces are obtained by real interpolation between L^p and W^1,p; Han-Sawyer introduced Besov spaces B^alpha,p,q for normal spaces of homogeneous type; We prove an embedding result in these particular Besov spaces. HS Han, Y., Sawyer, E., Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces. Mem. Amer. Math. Soc., vol. 110, no.530 (1994). Sh Shanmugalingam, N., Newtonian spaces: an extension of Sobolev spaces to metric measure spaces, Rev. Mat. Iberoamericana vol. 16, no.2 (2000).