Characterisations of Hardy growth spaces with doubling weights (Q2922941)

The aim of this paper is to obtain some characterizations of Hardy growth spaces with doubling weights. Two known results about Hardy growth spaces are generalized to a characterization of the Hardy growth spaces with doubling weights (Theorem 3.2). To obtain this, the blocking technique is used. The paper presents in the first section the necessary definitions for Hardy growth spaces, blocking technique, and doubling weights, and in the second section doubling weights as lacunary series with positive coefficients are analyzed. The main result is obtained in the third section, using the associated Fourier blocks to characterize Hardy growth spaces. The last section contains applications of the obtained results to characterize the Hadamard lacunary series in Hardy growth spaces and the solid hull of Hardy growth spaces.