BOUNDEDNESS AND CONTINUITY FOR VARIATION OPERATORS ON THE TRIEBEL-LIZORKIN SPACES

被引：0

作者：

Liu, Feng ^{[1
]}

Wen, Yongming ^{[2
]}

Zhang, Xiao ^{[3
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Minnan Normal Univ, Sch Math & Stat, Zhangzhou 363000, Fujian, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Elect & Informat Engn, Qingdao 266590, Shandong, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2022年 / 59卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Variation operator; commutator; Triebel-Lizorkin space; boundedness and continuity; WEIGHTED VARIATION INEQUALITIES; ROUGH SINGULAR-INTEGRALS; DIFFERENTIAL-OPERATORS; P-VARIATION;

D O I：

10.4134/BKMS.b210874

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish the boundedness and continuity for variation operators for theta-type Calderon-Zygmund singular integrals and their commutators on the Triebel-Lizorkin spaces. As applications, we obtain the corresponding results for the Hilbert transform, the Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators.

引用

页码：1539 / 1555

页数：17

共 28 条

[1] Variation in probability, ergodic theory and analysis [J].

Akcoglu, MA ;

Jones, RL ;

Schwartz, PO .

ILLINOIS JOURNAL OF MATHEMATICS, 1998, 42 (01) :154-177

[2] BOUNDEDNESS OF ROUGH INTEGRAL OPERATORS ON TRIEBEL-LIZORKIN SPACES [J].

Al-Qassem, H. M. ;

Cheng, L. C. ;

Pan, Y. .

PUBLICACIONS MATEMATIQUES, 2012, 56 (02) :261-277

[3]

BOURGAIN J, 1989, PUBL MATH-PARIS, P5

[4] Rough singular integrals on Triebel-Lizorkin space and Besov space [J].

Chen, Yanping ;

Ding, Yong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 347 (02) :493-501

[5] Variational inequalities for the commutators of rough operators with BMO functions [J].

Chen, Yanping ;

Ding, Yong ;

Hong, Guixiang ;

Liu, Honghai .

SCIENCE CHINA-MATHEMATICS, 2021, 64 (11) :2437-2460

[6] Rough singular integrals supported on submanifolds [J].

Chen, Yanping ;

Ding, Yong ;

Liu, Honghai .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 368 (02) :677-691

[7]

Cruz-Uribe D, 2005, INT MATH RES NOTICES, V2005, P1849

[8]

Frazier M., 1991, CBMS Regional Conference Series in Mathematics, V79, DOI [10.1090/cbms/079, DOI 10.1090/CBMS/079]

[9]

Grafakos L, 2008, GRAD TEXTS MATH, V249, P1, DOI 10.1007/978-0-387-09432-8_1

[10]

Korry S., 2002, Rev. Mat. Complut., V15, P401, DOI DOI 10.5209/REV_REMA.2002.V15.N2.16899

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