Regularity of integral operators (Q1881581)

The article aims on providing a proper analogue to the Hörmander condition for an integral operator to be bounded \(L^p\rightarrow I_\alpha(L^p)\), where the Sobolev space \(I_\alpha(L^p)\) is the image of \(L^p\) under the convolution with the Riesz potential \(I_\alpha: f\rightarrow (| \xi| ^{-\alpha} \widehat{f})^\vee\). Besides the general result, some particular cases of interest are presented in detail.