Isomorphisms on weighed banach spaces of harmonic and holomorphic functions

For an arbitrary open subset u ⊂ rd or u ⊂ ⊂d and a continuous function v:u→]0,∞[ we show that the space h v0(u) of weighed harmonic functions is almost isometric to a (closed) subspace of c0,thus extending a theorem due to bonet and wolf for spaces of holomorphic functions hv0(u) on open sets u⊂ d. inspired by recent work of boyd and rueda,we characterize in terms of the extremal points of the dual of hv0(u) when hv0(u) is isometric to a subspace of c0. some geometric conditions on an open set u⊂d and convexity conditions on a weight v on u are given to ensure that neither hv0(u) nor hv0(u) are rotund. © 2013 enrique jordá and ana maría zarco.