Revista de la
Unión Matemática Argentina
On fractional operators with more than one singularity
María Silvina Riveros and Raúl E. Vidal
Volume 66, no. 1 (2023), pp. 281–295    

https://doi.org/10.33044/revuma.4364

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Abstract

Let $0\leq \alpha < n$, $m\in \mathbb{N}$ and let $T_{\alpha,m}$ be an integral operator given by a kernel of the form \[K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),\] where $A_i$ are invertible matrices and each $k_i$ satisfies a fractional size and a generalized fractional Hörmander condition that depends on $\alpha$. In this survey, written in honour to Eleonor Harboure, we collect several results about boundedness in different spaces of the operator $T_{\alpha,m}$, obtained along the last 35 years by several members of the Analysis Group of FAMAF, UNC.

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