A Remark on a Maximal Operator for Fourier Multipliers

Abstract

For a finite set $\Lambda$ on the circle we consider a family of the multiplier operators $T_m$ in $l_2 ({\mathbb Z})$ generated by the $2^{-m}$-neighborhoods of $\Lambda$. We show that the norm of the corresponding maximal operator $T$ can not be estimated by an absolute constant.