Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

• Autorzy: Ali Akbulut , Amil Hasanov
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels [...] TΩ,αA1,A2,…,Ak, $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators [...] TΩ,αA1,A2,…,Ak, $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ from [...] Mp,φ1wptoMp,φ2wq ${M_{p,{\varphi _1}}}\left( {{w^p}} \right)\,{\rm{to}}\,{M_{p,{\varphi _2}}}\left( {{w^q}} \right)$ for 1 < p < q < ∞. In all cases the conditions for the boundedness of the operator [...] TΩ,αA1,A2,…,Ak, $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2) and w, which do not assume any assumption on monotonicity of ϕ1 (x,r), ϕ2(x, r) in r.

Słowa kluczowe

EN

Fractional multilinear integral; Rough kernel; BMO; Generalized weighted Morrey space

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 47G10: Integral operators
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 1023-1038

Daty

wydano

2016-01-01

otrzymano

2016-04-01

zaakceptowano

2016-11-02

online

2016-12-17

Twórcy

autor

Ali Akbulut

• Department of Mathematics, Ahi Evran University, Kirsehir,

autor

Amil Hasanov

• Amil Hasanov, Gandja State University, Gandja,

Identyfikatory

DOI

10.1515/math-2016-0090