Sequences of dilations and translations equivalent to the Haar system in $L^p$-spaces

Sergey V. Astashkin, Pavel A. Terekhin

Let $f={\sum }_{k=0}^{\infty }{c}_k{h}_{2^k}$, where $\{h_n\}$ is the classical Haar system, $c_k\in \mathbb{C}$. Given a $p\in (1,\infty )$, we find the sharp conditions, under which the se…