i'm just so concerned because some integrals of functions become finite because of the domain restrictions...
ok. i'll try thinking of a spherically symmetric func, to make things simpler.
@dick
i was just thinking in terms of x,y to make things easier to imagine. i restricted my domain as a unit circle in the x,y plane.
an unbounded f that is square integrable on a unit sphere...
****
thinking thinking thinking...
f(x,y)=exp(1/xy)?
?? it is unbounded as x,y approaches 0...
L_{\infty} = inf{C>=0: |f(x)| <=C for almost every x}
f is an element of L_{\infty}=||f||p as p approaches infinity is finite
from here, we derived the fact that the function u that we stated is of a p-series with p<1 for L2, therefore, the integration is finite. therefore is an element of L2...
Homework Statement
Construct a function u of the space H'(B), where B is a unit sphere in R^3, which does not belong to L∞(B).
Homework Equations
(relevant facts)
all L2 are hilbert, therefore the problem reduces for us finding an L2 function which is not L-infinity.
The Attempt...