On a vector-valued Hopf-Dunford-Schwartz lemma

被引：3

作者：

Charpentier, S. ^{[1
]}

Deleaval, L. ^{[2
]}

机构：

[1] Univ Lille 1, UMR 8524, Lab Paul Painleve, F-59650 Villeneuve Dascq, France

[2] Univ Paris 06, Inst Math Jussieu, F-75005 Paris, France

来源：

POSITIVITY | 2013年 / 17卷 / 03期

关键词：

Maximal ergodic theorem; Semi-group; Dunkl analysis; DUNKL OPERATORS; MAXIMAL INEQUALITIES; TRANSFORM; THEOREM; SPACES;

D O I：

10.1007/s11117-012-0211-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fefferman-Stein inequalities in the setting of Dunkl analysis where covering methods are not available.

引用

页码：899 / 910

页数：12

共 26 条

[1]

[Anonymous], 1970, ANN MATH STUD

[2]

[Anonymous], DEGRUYTER STUDIES MA

[3] TRANSFERENCE OF STRONG TYPE MAXIMAL INEQUALITIES BY SEPARATION-PRESERVING REPRESENTATIONS [J].

ASMAR, N ;

BERKSON, E ;

GILLESPIE, TA .

AMERICAN JOURNAL OF MATHEMATICS, 1991, 113 (01) :47-74

[4] ON ERGODIC THEOREM WITHOUT ASSUMPTION OF POSITIVITY [J].

CHACON, RV .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1961, 67 (02) :186-&

[5] FACTORIZATION THEORY AND AP WEIGHTS [J].

DEFRANCIA, JLR .

AMERICAN JOURNAL OF MATHEMATICS, 1984, 106 (03) :533-547

[6] THE DUNKL TRANSFORM [J].

DEJEU, MFE .

INVENTIONES MATHEMATICAE, 1993, 113 (01) :147-162

[7] Two results on the Dunkl maximal operator [J].

Deleaval, Luc .

STUDIA MATHEMATICA, 2011, 203 (01) :47-68

[8] Fefferman-Stein inequalities for the Z2d Dunkl maximal operator [J].

Deleaval, Luc .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 360 (02) :711-726

[9]

Dunford N., 1958, Pure and Applied Mathematics

[10] DIFFERENTIAL-DIFFERENCE OPERATORS ASSOCIATED TO REFLECTION GROUPS [J].

DUNKL, CF .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 311 (01) :167-183

← 1 2 3 →