BOUNDEDNESS OF SUBLINEAR-OPERATORS IN HERZ SPACES ON VILENKIN GROUPS AND ITS APPLICATION

The authors establish the boundedness of some sublinear operators in w eighted Herz spaces on Vilenkin groups under certain weak local hypoth eses on the size of these operators at the identity. This class of ope rators includes most of the important operators in harmonic analysis o n Vilenkin groups. The main theorems are best possible under the condi tions of the theorems. As applications, the authors establish the Litt lewood-Paley function characterization of some Herz spaces and the rel ations between Herz spaces and Herz-type Hardy spaces.