Multiresolution and Approximation and Hardy Spaces

Abstract

In this paper we show that with the help of the Marcinkiewicz average of orthogonal projections on multiresolution approximation ofLp(Rn) forp⩽1 built by a box spline one can construct equivalent metric in Hardy spaces. To prove this equivalence we generalize Fefferman–Stein theorem for discrete choice of parametert. It turns out that the Marcinkiewicz average of the Ciesielski–Dürmeyer operator has similar properties as orthogonal projection.