Outer measures and weak type (1,1) estimates of HardyLittlewood maximal operators
Preprint Series # 692 Terasawa, Yutaka Outer measures and weak type (1,1) estimates of HardyLittlewood maximal operators. (2004); Abstract We will introduce the $k$ times modified centered and uncentered
HardyLittlewood maximal operators
on nonhomogeneous spaces for $k>0$. We will prove the $k$ times
modified centered HardyLittlewood 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 HardyLittlewood maximal
operators on homogeneous spaces and on the real
line by using outer measures. Item Type:  Preprint 

Additional Information:  40 

Uncontrolled Keywords:  HardyLittlewood maximal operator,
weak type $(1,1)$ estimate, operator norm, outer measure 

Subjects:  42xx FOURIER ANALYSIS 

ID Code:  858 

