Affiliation:
1. College of Mathematics and Statistics , Northwest Normal University , Lanzhou , Gansu 730070 , P. R. China
Abstract
Abstract
This paper is devoted to studying the regularity properties for the new maximal operator
M
φ
{M_{\varphi}}
and the fractional new maximal operator
M
φ
,
β
{M_{\varphi,\beta}}
in the local case. Some new pointwise gradient estimates of
M
φ
,
Ω
{M_{\varphi,\Omega}}
and
M
φ
,
β
,
Ω
{M_{\varphi,\beta,\Omega}}
are given. Moreover, the boundedness of
M
φ
,
Ω
{M_{\varphi,\Omega}}
and
M
φ
,
β
,
Ω
{M_{\varphi,\beta,\Omega}}
on Sobolev space is established. As applications, we also obtain the bounds of the above operators on Sobolev space with zero boundary values.
Funder
National Natural Science Foundation of China
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