Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

100%

Akbulut A., Hasanov A.

Open Mathematics

2016

tom 14

nr 1

1023-1038

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.

A new approach to nonlinear singular integral operators depending on three parameters

100%

Uysal G.

Open Mathematics

2016

tom 14

nr 1

897-907

In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , $${T_\lambda }(f;x,y) = \iint\limits_{{\mathbb{R}^2}} {(t - x,s - y,f(t,s))dsdt,\;(x,y) \in {\mathbb{R}^2},\lambda \in \Lambda ,}$$ where Λ is a set of non-negative numbers with accumulation point λ0.

Ograniczanie wyników

2 Open Mathematics

1 Akbulut A.

1 Hasanov A.

1 Uysal G.

2 2016

Wyniki wyszukiwania

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

A new approach to nonlinear singular integral operators depending on three parameters