On inequivalences of sequences of characters

Abstract

We establish various results including the following: if $1<p<\infty$ and $\sigma$ is a bijection between the trigonometric functions on $[0,1)$ and the Walsh functions on $[0,1)$. Then $\sigma$ does not extend to an isomorphism $L_p[0,1)\to L_p[0,1)$.

arXiv comment11 pp; corrected errors including an error in the second application which now leads to weaker bounds. Details are given at the end of the paper