2018
Том 70
№ 9

Multiple Haar Basis and its Properties

Romanyuk V. S.

Abstract

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 $L_p ([0, 1]^d ),\; 1 ≤ p < ∞$.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 9, pp 1411-1424.

Citation Example: Romanyuk V. S. Multiple Haar Basis and its Properties // Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1253–1264.

Full text