Due March 23
If is a family of better kernels, there exists a constant such that
for all .
For , let
- f is of bounded variation iff .
- For each , construct an -Hölder continuos function that is not of bounded variation.
- If , f’ exists at every point but is not integrable.
Define the one-sided maximal function for locally integrable functions on as
If , then
Let be absolutely continuous.
- f maps sets of measure zero to sets of measure 0.
- f maps measurable sets to measurable sets.