Fractional Integration on Mixed Norm Spaces. I

Feng Guo; Xiang Fang; Shengzhao Hou; Xiaolin Zhu

doi:10.1007/s11785-024-01488-3

Fractional Integration on Mixed Norm Spaces. I

Feng Guo, Xiang Fang, Shengzhao Hou, Xiaolin Zhu

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

摘要

In this paper we characterize completely the septuple (Formula presented.) such that the fractional integration operator I_t, of order t∈C, is bounded between two mixed norm spaces: (Formula presented.) We treat three types of definitions for I_t: Hadamard, Flett, and Riemann-Liouville. Our main result (Theorem 2) extends that of Buckley-Koskela-Vukotić in 1999 on the Bergman spaces (Theorem B), and the case t=0 recovers the embedding theorem of Arévalo in 2015 (Corollary 3). The corresponding result for the Hardy spaces H^p(D), of type Riemann-Liouville, is due to Hardy and Littlewood in 1932.

原文	???core.languages.en_GB???
文章編號	45
期刊	Complex Analysis and Operator Theory
卷	18
發行號	3
DOIs	https://doi.org/10.1007/s11785-024-01488-3
出版狀態	已出版 - 4月 2024

存取文件

10.1007/s11785-024-01488-3

引用此

@article{9c49228da90b42ea9a349e4bb1e89d94,

title = "Fractional Integration on Mixed Norm Spaces. I",

abstract = "In this paper we characterize completely the septuple (Formula presented.) such that the fractional integration operator It, of order t∈C, is bounded between two mixed norm spaces: (Formula presented.) We treat three types of definitions for It: Hadamard, Flett, and Riemann-Liouville. Our main result (Theorem 2) extends that of Buckley-Koskela-Vukoti{\'c} in 1999 on the Bergman spaces (Theorem B), and the case t=0 recovers the embedding theorem of Ar{\'e}valo in 2015 (Corollary 3). The corresponding result for the Hardy spaces Hp(D), of type Riemann-Liouville, is due to Hardy and Littlewood in 1932.",

keywords = "26A33, 47B38, Fractional integration, Mixed norm space, Riemann-Liouville",

author = "Feng Guo and Xiang Fang and Shengzhao Hou and Xiaolin Zhu",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.",

year = "2024",

month = apr,

doi = "10.1007/s11785-024-01488-3",

language = "???core.languages.en_GB???",

volume = "18",

journal = "Complex Analysis and Operator Theory",

issn = "1661-8254",

number = "3",

}

TY - JOUR

T1 - Fractional Integration on Mixed Norm Spaces. I

AU - Guo, Feng

AU - Fang, Xiang

AU - Hou, Shengzhao

AU - Zhu, Xiaolin

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

PY - 2024/4

Y1 - 2024/4

N2 - In this paper we characterize completely the septuple (Formula presented.) such that the fractional integration operator It, of order t∈C, is bounded between two mixed norm spaces: (Formula presented.) We treat three types of definitions for It: Hadamard, Flett, and Riemann-Liouville. Our main result (Theorem 2) extends that of Buckley-Koskela-Vukotić in 1999 on the Bergman spaces (Theorem B), and the case t=0 recovers the embedding theorem of Arévalo in 2015 (Corollary 3). The corresponding result for the Hardy spaces Hp(D), of type Riemann-Liouville, is due to Hardy and Littlewood in 1932.

AB - In this paper we characterize completely the septuple (Formula presented.) such that the fractional integration operator It, of order t∈C, is bounded between two mixed norm spaces: (Formula presented.) We treat three types of definitions for It: Hadamard, Flett, and Riemann-Liouville. Our main result (Theorem 2) extends that of Buckley-Koskela-Vukotić in 1999 on the Bergman spaces (Theorem B), and the case t=0 recovers the embedding theorem of Arévalo in 2015 (Corollary 3). The corresponding result for the Hardy spaces Hp(D), of type Riemann-Liouville, is due to Hardy and Littlewood in 1932.

KW - 26A33

KW - 47B38

KW - Fractional integration

KW - Mixed norm space

KW - Riemann-Liouville

UR - http://www.scopus.com/inward/record.url?scp=85186402137&partnerID=8YFLogxK

U2 - 10.1007/s11785-024-01488-3

DO - 10.1007/s11785-024-01488-3

M3 - 期刊論文

AN - SCOPUS:85186402137

SN - 1661-8254

VL - 18

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 3

M1 - 45

ER -

Fractional Integration on Mixed Norm Spaces. I

摘要

存取文件

指紋

引用此