Equivalence of norms of the generalized fractional integral operator and the generalized fractional maximal operator on the generalized weighted Morrey spaces
Annals of Functional Analysis, cilt.11, sa.4, ss.1007-1026, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 4
- Basım Tarihi: 2020
- Doi Numarası: 10.1007/s43034-020-00066-w
- Dergi Adı: Annals of Functional Analysis
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
- Sayfa Sayıları: ss.1007-1026
- Anahtar Kelimeler: Generalized fractional integral operator, Generalized fractional maximal operator, Generalized weighted Morrey spaces, Muckenhoupt class, Sharp maximal function
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Hayır
Özet
© 2020, Tusi Mathematical Research Group (TMRG).The goal of this paper is to characterize the local sharp estimate (Iρf)#(x)≤CMρf(x) and by using this inequality to get necessary and sufficient conditions on the triple functions (φ, ρ, ω) which satisfy the equivalence of norms of the generalized fractional integral operator Iρ and the generalized fractional maximal operator Mρ on the generalized weighted Morrey spaces Mp,φ(Rn, ω) and generalized weighted central Morrey spaces M˙ p,φ(Rn, ω) , when ω∈ A∞-Muckenhoupt class.