We study function multipliers between spaces of holomorphic functions on the unit disc of the complex plane generated by symmetric sequence spaces. In the case of sequence   $\ell ^{p}$  spaces we recover Nikol’skii’s results [‘Spaces and algebras of Toeplitz matrices operating on
 $\ell ^{p}$  spaces we recover Nikol’skii’s results [‘Spaces and algebras of Toeplitz matrices operating on   $\ell ^{p}$ ’, Sibirsk. Mat. Zh.7 (1966), 146–158].
 $\ell ^{p}$ ’, Sibirsk. Mat. Zh.7 (1966), 146–158].