Regularity of averages over hypersurfaces (Q756065)

The author studies averages over smooth measures on smooth compact hypersurfaces in \({\mathbb{R}}^ n\). His results are closely related to the recent works of \textit{L. Colzani} [J. Aust. Math. Soc., Ser. A 41, 287-297 (1986; Zbl 0616.43010)], \textit{M. Cowling} and \textit{G. Mauceri} [Trans. Am. Math. Soc. 296, 341-365 (1986; Zbl 0651.42007)] and \textit{J. L. Rubio de Francia} [Duke Math. J. 53, 395-404 (1986; Zbl 0612.42008)]. If some assumptions are made on the decay of the Fourier transform of the measure defining the averages, then mixed norm estimates for these means can be obtained. As a consequence, \(L^ p\) estimates of multiparameter maximal functions are obtained.