Multiple Haar Basis and its Properties - Romanyuk, V. S. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
In the Lebesgue spaces L_p ([0, 1]^d ), 1 ≤ p ≤ ∞, for d ≥ 2, we define a multiple basis system of functions H^d = (h_n )_n = 1^∞. This system has the main properties of the well-known one-dimensional Haar basis H. In particular, it is shown that the system H^d is a Schauder basis in the spaces L_p ([0, 1]^d ), 1 ≤ p