Adaptive Fourier decomposition in H p

In this paper, we study decomposition of functions in Hardy spaces H p ( T ) ( 1 < p < ∞ ) . First, we will give a direct application of adaptive Fourier decomposition (AFD) of H 2 ( T ) to functions in H p ( T ) . Then, we study adaptive decomposition by the system 1 D : =e a ( z ) =A a , p1 − ā z , a ∈ D , where A a , p is the normalization factor making e a ( z ) to be of unit p ‐norm. Under the proposed decomposition procedure, we show that every f ∈ H p ( T ) can be effectively expressed by a linear combination of{ ea n( z ) } n = 1 + ∞ . We give a maximal selection principle ofea nat the n th step and prove the convergence.