MAXIMAL AVERAGES ALONG A PLANAR VECTOR FIELD DEPENDING ON ONE VARIABLE

被引：5

作者：

Bateman, Michael ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2013年 / 365卷 / 08期

关键词：

ARBITRARY SETS; DIRECTIONS; OPERATORS;

D O I：

10.1090/S0002-9947-2013-05673-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove (essentially) sharp L-2 estimates for a restricted maximal operator associated to a planar vector field that depends only on the horizontal variable. The proof combines an understanding of such vector fields from earlier work of the author with a result of Nets Katz on directional maximal operators.

引用

页码：4063 / 4079

页数：17

共 8 条

[1]

Bateman M, 2009, P AM MATH SOC, V137, P955

[2]

Duoandikoetxea Javier, 2001, AMS GRADUATE STUDIES, V29

[3]

Fefferman C., ANN MATH, V98, P551

[4] Remarks on maximal operators over arbitrary sets of directions [J].

Katz, NH .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1999, 31 :700-710

[5] Maximal operators over arbitrary sets of directions [J].

Katz, NH .

DUKE MATHEMATICAL JOURNAL, 1999, 97 (01) :67-79

[6]

Lacey M., 2010, MEMOIRS AMS, V205, DOI 10.1090/S0065-9266-10-00572-7.

[7]

LACEY M, LIPSCHITZ VARIANT KA

[8] Maximal theorems for the directional Hilbert transform on the plane [J].

Lacey, Michael T. ;

Li, Xiaochun .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (09) :4099-4117

← 1 →