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THE `UNCENTERED' MAXIMAL FUNCTION AND Lp-BOUNDEDNESS
 

Summary: THE `UNCENTERED' MAXIMAL FUNCTION
AND Lp-BOUNDEDNESS
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 weak-type p; p for any dimension n.
Let := x;y, where x 2 Rn and y is real. Now, introduce the uncentered"
weighted-Maximal 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:

  

Source: Amdeberhan, Tewodros - Department of Mathematics, Tulane University

 

Collections: Mathematics