Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators
Preprint Series # 692
Terasawa, Yutaka Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators. (2004);
We will introduce the $k$ times modified centered and uncentered
Hardy-Littlewood maximal operators
on nonhomogeneous spaces for $k>0$. We will prove the $k$ times
modified centered Hardy-Littlewood maximal operator
is weak type $(1,1)$ bounded with constant $1$ when
$k \ge 2$ if the Radon measure
of the space has ``continuitiy'' in some sense.
In the proof, we will use the outer measure
associated with the Radon measure.
We will also prove other results of Hardy-Littlewood maximal
operators on homogeneous spaces and on the real
line by using outer measures.
|Uncontrolled Keywords:|| Hardy-Littlewood maximal operator,
weak type $(1,1)$ estimate, operator norm, outer measure|
|Subjects:||42-xx FOURIER ANALYSIS|