Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Ali Akbulut; Amil Hasanov

Open Mathematics, Tome 14 (2016), p. 1023-1038 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels [...] TΩ,αA1,A2,…,Ak, $T_{Ω, α}^{A_{1}, A_{2}, ..., A_{k}},$ 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, $T_{Ω, α}^{A_{1}, A_{2}, ..., A_{k}},$ from [...] Mp,φ1wptoMp,φ2wq $M_{p, ϕ_{1}} (w^{p}) to M_{p, ϕ_{2}} (w^{q})$ for 1 < p < q < ∞. In all cases the conditions for the boundedness of the operator [...] TΩ,αA1,A2,…,Ak, $T_{Ω, α}^{A_{1}, A_{2}, ..., A_{k}},$ 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.

Publié le : 2016-01-01

Zbl 1355.42005

EUDML-ID : urn:eudml:doc:287150

@article{bwmeta1.element.doi-10_1515_math-2016-0090,
     author = {Ali Akbulut and Amil Hasanov},
     title = {Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces},
     journal = {Open Mathematics},
     volume = {14},
     year = {2016},
     pages = {1023-1038},
     zbl = {1355.42005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0090}
}

Ali Akbulut; Amil Hasanov. Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces. Open Mathematics, Tome 14 (2016) pp. 1023-1038. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0090/