An Interpolation Theorem beetwen weighted Hardy spaces

SHELDY OMBROSI, CARLOS SEGOVIA, RICARDO TESTONI

ARKIV FOR MATEMATIK

Springer Netherlands

Lugar: Dordrecht The Netherlands; Año: 2006 vol. 1 p. 335 - 348

0004-2080

In this paper we generalize an interpolation result due to J.-O. Strömberg and A. Torchinsky to the case of one-sided Hardy spaces. This generalization is important in the study of the weak type (1,1) for lateral strongly singular operators. We shall need an atomic decomposition in which for every atom there exists another atom supported contiguously at its right. In order to obtain this decomposition we have developed a rather simple technique to break up an atom into a sum of others atoms.