In this paper we study a family of singular integral operators that generalizes the higher order Gaussian Riesz Transforms and find the right weight w to make them continuous from L 1(wdγ) into L 1, ∞ (dγ), being dg(x)=e-|x|2dx.dgamma(x)=e^{-|x|^2}dx. Some boundedness properties of these operators had already been derived by Urbina (Ann Scuola Norm Sup Pisa Cl Sci 17(4):531–567, 1990) and Pérez (J Geom Anal 11(3):491–507, 2001).
展开▼
机译：在本文中，我们研究了一类奇异积分算子，该算子推广了高阶高斯Riesz变换，并找到合适的权重w使它们从L 1 （wdγ）连续变为L 1，∞ （dγ），即dg（x）= e -| x | 2 dx.dgamma（x）= e ^ {-| x | ^ 2 } dx。这些算子的一些有界性质已经由Urbina（Ann Scuola Norm Sup Pisa Cl Sci 17（4）：531-567，1990）和Pérez（J Geom Anal 11（3）：491-507，2001）导出。
展开▼
