Let
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H(\mathbb{D})$
denote the space of holomorphic functions on the unit disc
$\mathbb{D}$
. Given
$p>0$
and a weight
$\omega $
, the Hardy growth space
$H(p, \omega )$
consists of those
$f\in H(\mathbb{D})$
for which the integral means
$M_p(f,r)$
are estimated by
$C\omega (r)$
,
$0<r<1$
. Assuming that
$p>1$
and
$\omega $
satisfies a doubling condition, we characterise
$H(p, \omega )$
in terms of associated Fourier blocks. As an application, extending a result by Bennett et al. [‘Coefficients of Bloch and Lipschitz functions’, Illinois J. Math. 25 (1981), 520–531], we compute the solid hull of
$H(p, \omega )$
for
$p\ge 2$
.