 
Summary: THE `UNCENTERED' MAXIMAL FUNCTION
AND LpBOUNDEDNESS
Tewodros Amdeberhan
Department of Mathematics, Temple University, Philadelphia PA 19122
tewodros@euclid.math.temple.edu
Abstract. In this note, we prove that the `uncentered' Maximal function is not a
bounded operator from Lpd to Lpd, when d is the Gaussian measure on Rn.
In fact, it is not even weaktype p; p for any dimension n.
Let := x;y, where x 2 Rn and y is real. Now, introduce the uncentered"
weightedMaximal function
Mf := supB
1
B
Z
B
jfjd;
where the supremum runs over all euclidean balls B containing , and the integral is
taken with respect to the Gaussian measure
d := e,jj2=2
d:
