The Criteria Of Harmonic α-Bloch Function And Harmonic Little α-Bloch Function

In 1999, Pengcheng Wu studied the characterization for harmonic Bloch functions, harmonic little Bloch functions and harmonic normal functions by means of increasing functions. In his paper "Increasing Functions, Harmonic Bloch and Harmonic Normal Functions " . In 2001, Pengcheng Wu and Hasi Wulan formally introduce the Q_K spaces in their paper Characterizations of Q_K spaces . In this paper,Corresponding to results of the paper Increasing Functions, Harmonic Bloch and Harmonic Normal Functions, adding the condition ofα(0<α<∞), we shall discuss characterizations of harmonicα-Bloch function and harmonic littleα-Bloch function are given by means of increasing functions. For the results of paper Characterizations of Q_K spaces, we shall introduce some new function spaces: they are Q_T,α^h space, Q_p,α^h space, Q_T,h^# space and Q_p,h^# space. We will study the relation of Q_T,α^h space and Q_p,α^h space and the relation of Q_T,h^# space and Q_p,h^# space, we will get some new useful results whom extend earlier results.