Sampling, Marcinkiewicz-Zygmund Inequalities, Approximation, and Quadrature Rules
Karlheinz Groechenig
Abstract: Given a sequence of Marcinkiewicz-Zygmund inequalities in L2 , we derive approximation theorems and quadrature rules. The derivation is completely elementary and requires only the definition of Marcinkiewicz-Zygmund inequality, Sobolev spaces, and the solution of least square problems. We briefly discuss the existence and construction of Marcinkiewicz-Zygmund inequalities in Bergman and Hardy spaces.