GENERAL FORM OF LINEAR FUNCTIONALS ON HARDY SPACES

Bui Khoi Dam

Abstract

           In this note, we give a general form of linear functionals on martingale Hardy spaces H_Φ, where the Young function Φ has finite power and its conjugate function Ψ is of the form Ψ(x) = Ψ₁(x²) with &Psi:₁} being also a Young function. Moreover, we discuss the relationship between the martingale Hardy space H_Φ and the spaces K_Ψ.