Weak and strong type inequalities criteria for fractional maximal functions and fractional integrals associated with Gegenbauer differential operator

被引：2
|
作者：
Kokilashvili, Vakhtang [2 ]
Ibrahimov, Elman J. [1 ]
机构：
[1] ANAS, Inst Math & Mech, Baku, Azerbaijan
[2] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, Tbilisi, Georgia
来源：
GEORGIAN MATHEMATICAL JOURNAL | 2023年 / 30卷 / 05期
关键词：
Young function; Banach function spaces; G-Orlicz space; G-maximal function; G-fractional integral; ORLICZ; BOUNDEDNESS; THEOREM;
D O I：
10.1515/gmj-2023-2031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper deals with the introduction and study of a new, Orlicz type space associated with the Gegenbauer differential operator and briefly called here a G-Orlicz space. We prove that such spaces are Banach function spaces. The necessary and sufficient conditions are established which ensure the validity of weak and strong type inequalities for fractional maximal functions and fractional integrals of G-Orlicz spaces.
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页码：745 / 767
页数：23
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