Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Ali Akbulut, and Amil Hasanov. "Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces." Open Mathematics 14.1 (2016): 1023-1038. <http://eudml.org/doc/287150>.

@article{AliAkbulut2016,
abstract = {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.},
author = {Ali Akbulut, Amil Hasanov},
journal = {Open Mathematics},
keywords = {Fractional multilinear integral; Rough kernel; BMO; Generalized weighted Morrey space; fractional multilinear integral operators; rough kernel; BMO space; generalized weighted Morrey space},
language = {eng},
number = {1},
pages = {1023-1038},
title = {Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces},
url = {http://eudml.org/doc/287150},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Ali Akbulut
AU - Amil Hasanov
TI - Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 1023
EP - 1038
AB - 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.
LA - eng
KW - Fractional multilinear integral; Rough kernel; BMO; Generalized weighted Morrey space; fractional multilinear integral operators; rough kernel; BMO space; generalized weighted Morrey space
UR - http://eudml.org/doc/287150
ER -