Sobolev Spaces
The Soblev spaces are space of functions wich derivate up to order k belongs to Lp, formally
Wk, p = {f∈Lp | Dα f ∈Lp, |∈|≤k}
Sobolev espaces are subespaces of Lp, in particular.
Wk, p ⊂ Lp
from this viewpoint
Lp = W0,p
Also, there is a definition in the Fourier Coefficents framework, if f^n is the n-th Fourier coefficient, then
The Soblev spaces are space of functions wich derivate up to order k belongs to Lp, formally
Wk, p = {f∈Lp | Dα f ∈Lp, |∈|≤k}
Sobolev espaces are subespaces of Lp, in particular.
Wk, p ⊂ Lp
from this viewpoint
Lp = W0,p
Also, there is a definition in the Fourier Coefficents framework, if f^n is the n-th Fourier coefficient, then
