Vector valued q-variation for ergodic averages and analytic semigroups

被引：16

作者：

Hong, Guixiang ^{[1
,2
]}

Ma, Tao ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] CSIC, CSIC UAM UCM UC3M, Inst Ciencias Matemat, C Nicolas Cabrera 13-15, Madrid, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 437卷 / 02期

关键词：

Variational inequalities; UMD lattices; Ergodic averages; Analytic semigroups; Pointwise convergence rate; Extrapolation; WEIGHTED VARIATION INEQUALITIES; SINGULAR-INTEGRALS; L-P; DIFFERENTIAL-OPERATORS; OSCILLATION; THEOREMS;

D O I：

10.1016/j.jmaa.2016.01.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish UMD lattice-valued variational inequalities for ergodic averages of contractively regular operators and analytic semigroups. These results generalize, on the one hand some scalar-valued variational inequalities in ergodic theory, on the other hand Xu's very recent result on UMD lattice-valued maximal inequality. As an application, we deduce the jump estimates and obtain quantitative information on the rate of the pointwise convergence for semigroups acting on UMD lattice-valued functions. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：1084 / 1100

页数：17

共 39 条

[1]

[Anonymous], 1991, Banach lattices

[2] STECKINS THEOREM, TRANSFERENCE, AND SPECTRAL DECOMPOSITIONS [J].

BERKSON, E ;

GILLESPIE, TA .

JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 70 (01) :140-170

[3]

BOURGAIN J, 1989, PUBL MATH-PARIS, P5

[4]

Campbell JT, 2000, DUKE MATH J, V105, P59

[5] Oscillation and variation for singular integrals in higher dimensions [J].

Campbell, JT ;

Jones, RL ;

Reinhold, K ;

Wierdl, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (05) :2115-2137

[6] On a vector-valued Hopf-Dunford-Schwartz lemma [J].

Charpentier, S. ;

Deleaval, L. .

POSITIVITY, 2013, 17 (03) :899-910

[7] POINT WISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS [J].

Cowling, Michael G. ;

Leinert, Michael .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2011, 84 (01) :44-48

[8]

DEFRANCIA JLR, 1986, LECT NOTES MATH, V1221, P195

[9] Variational estimates for paraproducts [J].

Do, Yen ;

Muscalu, Camil ;

Thiele, Christoph .

REVISTA MATEMATICA IBEROAMERICANA, 2012, 28 (03) :857-878

[10]

Goldstein JA., 1985, Semigroups of Linear Operators and Applications

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