Abstract
We give analytic description for the completion of C?0 (R+) in Dirichlet
space D1,p(R+, ?) := {u : R+ -> R : u is locally absolutely continuous on R+ and ||u? ||_Lp(R+,?) < ?}, for given continuous
positive weight ? defined on R+, where 1 < p < ?. The conditions are described in terms of the modified variants of the Bp
conditions due to Kufner and Opic from 1984, which in our approach are focusing on integrability of ?^-p/(p-1) near zero or near infinity.
Moreover, we propose applications of our results to: obtaining new
variants of Hardy inequality, interpretation of boundary value problems in ODE's defined on the halpfline with solutions in D1,p(R+, ?),
new results from complex interpolation theory dealing with interpolation spaces between weighted Dirichlet spaces, and to derivation
of new Morrey type embedding theorems for our Dirichlet space.
Anno
2022
Autori IAC
Tipo pubblicazione
Altri Autori
Claudia Capone Agnieszka Kalamajska
Rivista
arXiv