Problem IV Let X be a Banach space, U R n be measurable, and 1 q1

7:00 NO $ 1.00 408% Math 554 Homework 4 Due October 30, 2008, before class Problem I Prove that WI,(R") - CO(R"). (Hint: use mollifiers but be careful because Co (IR" ) is NOT dense in WI. (R").) Problem II Let U C R" be bounded and 0 0 : (i) there exists a compact G C U such that If (2 )Piece vje s; (ii) there exists & > 0 such that for all he IR", [h)