Marcinkiewicz-Zygmund inequalities and the numerical approximation of singular integrals for exponential weights: methods, results and open problems, some new, some old

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 Oberwolfach workshop: ’Numerical integration and Complexity.’ 1991 AMS(MOS) Classification: 41A10, 42C05.