Generalized fractional integral operators on Orlicz-Hardy spaces

被引：7

作者：

Arai, Ryutaro ^{[1
]}

Nakai, Eiichi ^{[1
]}

Sawano, Yoshihiro ^{[2
,3
]}

机构：

[1] Ibaraki Univ, Dept Math, Mito, Ibaraki 3108512, Japan

[2] Chuo Univ, Dept Math, Bunkyo Ku, 1-13-27 Kasuga, Tokyo 1128551, Japan

[3] Peoples Friendship Univ Russia, RUDN Univ, Dept Math Anal & Theory Funct, 6 Miklukho Maklay St, Moscow 117198, Russia

来源：

MATHEMATISCHE NACHRICHTEN | 2021年 / 294卷 / 02期

基金：

日本学术振兴会;

关键词：

fractional integral operator; Hardy space; Orlicz–

D O I：

10.1002/mana.201900052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The generalized fractional integral operators are shown to be bounded from an Orlicz-Hardy space H phi(Rn) to another Orlicz-Hardy space H psi(Rn), where phi and psi are generalized Young functions. The result extends the boundedness of the usual fractional integral operator I alpha from Hp(Rn) to Hq(Rn) for alpha,p,q is an element of(0,infinity) and -n/p+alpha=-n/q, which was proved by Stein and Weiss in 1960.

引用

页码：224 / 235

页数：12

共 23 条

[11]

Nakai E, 2001, TAIWAN J MATH, V5, P587

[12] Orlicz-Hardy spaces and their duals [J].

Nakai, Eiichi ;

Sawano, Yoshihiro .

SCIENCE CHINA-MATHEMATICS, 2014, 57 (05) :903-962

[13] Hardy spaces with variable exponents and generalized Campanato spaces [J].

Nakai, Eiichi ;

Sawano, Yoshihiro .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (09) :3665-3748

[14] FRACTIONAL INTEGRATION IN ORLICZ SPACES .1. [J].

ONEIL, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 115 (03) :300-&

[15] SHARP L(P)-WEIGHTED SOBOLEV INEQUALITIES [J].

PEREZ, C .

ANNALES DE L INSTITUT FOURIER, 1995, 45 (03) :809-&

[16]

Pustylnik E., 1999, ISRAEL MATH C P, V13, P161

[17]

Sawano Y, 2018, DEV MATH, V56, DOI 10.1007/978-981-13-0836-9

[18] Generalized Fractional Integral Operators and Their Commutators with Functions in Generalized Campanato Spaces on Orlicz Spaces [J].

Shi, Minglei ;

Arai, Ryutaro ;

Nakai, Eiichi .

TAIWANESE JOURNAL OF MATHEMATICS, 2019, 23 (06) :1339-1364

[19]

Siddhamshetty P, 2017, P AMER CONTR CONF, P2182, DOI 10.23919/ACC.2017.7963276

[20]

Stein E.M, 1970, PRINCETON MATH SERIE, V30

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