TY - JOUR AU - V. S. Romanyuk PY - 2015/09/25 Y2 - 2024/03/29 TI - Multiple Haar Basis and its Properties JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 67 IS - 9 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2063 AB - 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