### 3 Classification des plongements isotropes d'après A. Weinstein

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This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball.

In [P] we characterize the pairs of weights for which the fractional integral operator ${I}_{\gamma}$ of order $\gamma $ from a weighted Lebesgue space into a suitable weighted $BMO$ and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of ${I}_{\gamma}$ acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare...

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 , $${T}_{\lambda}(f;x,y)=\underset{{\mathbb{R}}^{2}}{\phantom{\rule{0.277778em}{0ex}}\int \int \phantom{\rule{0.277778em}{0ex}}}(t-x,s-y,f(t,s))dsdt,\phantom{\rule{0.277778em}{0ex}}(x,y)\in {\mathbb{R}}^{2},\lambda \in \Lambda ,$$ where Λ is a set of non-negative numbers with accumulation point λ0.