*Correspondence: [email protected] 1School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China Full list of author information is available at the end of the article Abstract In this note we establish the Lp boundedness of Marcinkiewicz integrals with mixed homogeneity along compound surfaces, which improve and extend some previous results. The main ingredient is to presen...

In this short article, we explore some methods, results and open problems dealing with weighted Marcinkiewicz-Zygmund inequalities as well as the numerical approximation of integrals for exponential weights on the real line and on finite intervals of the line. The problems posed are based primarily on ongoing work of the author and his collaborators and were presented at the November 2001 Oberw...