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1
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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
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.
2
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A variant sharp estimate for multilinear singular integral operators

100%
Hu G., Yang D.
Studia Mathematica
|
2000
|
tom 141
|
nr 1
25-22
EN
We establish a variant sharp estimate for multilinear singular integral operators. As applications, we obtain the weighted norm inequalities on general weights and certain $Llog^{+}L$ type estimates for these multilinear operators.
3
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Weighted inequalities for some integral operators with rough kernels

100%
Riveros M., Urciuolo M.
Open Mathematics
|
2014
|
tom 12
|
nr 4
636-647
EN
In this paper we study integral operators with kernels $$K(x,y) = k_1 (x - A_1 y) \cdots k_m \left( {x - A_m y} \right),$$ $$k_i \left( x \right) = {{\Omega _i \left( x \right)} \mathord{\left/ {\vphantom {{\Omega _i \left( x \right)} {\left| x \right|}}} \right. \kern-\nulldelimiterspace} {\left| x \right|}}^{{n \mathord{\left/ {\vphantom {n {q_i }}} \right. \kern-\nulldelimiterspace} {q_i }}}$$ where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.
4
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Partial retractions for weighted Hardy spaces

100%
Kisliakov S., Xu Q.
Studia Mathematica
|
2000
|
tom 138
|
nr 3
251-264
EN
Let 1 ≤ p ≤ ∞ and let $w_0, w_1$ be two weights on the unit circle such that $log(w_0w_1^{-1})∈ BMO$. We prove that the couple $(H_p(w_0), H_p(w_1))$ of weighted Hardy spaces is a partial retract of $(L_p(w_0), L_p(w_1))$. This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.
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