Multiple Haar Basis and its Properties

• Datum: 2015
• Hauptverfasser: Romanyuk, V. S., Романюк, В. С.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2015
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/2063
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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...