Rademacher functions in Morrey spaces

The Rademacher sums are investigated in the Morrey spaces Mp,wMp,w on [0,1][0,1] for 1≤p<∞1≤p<∞ and weight w   being a quasi-concave function. They span l2l2 space in Mp,wMp,w if and only if the weight w   is smaller than log2−1/2⁡2t on (0,1)(0,1). Moreover, if 1