Results are obtained which relate the size of the coefficients
a
n
{a_n}
of an exponential series
f
(
x
)
=
Σ
n
=
0
∞
a
n
ε
−
Λ
n
x
,
x
>
0
,
Re
Λ
n
>
0
f(x) = \Sigma _{n = 0}^\infty {a_n}{\varepsilon ^{ - {\Lambda _n}x}},x > 0,\operatorname {Re} {\Lambda _n} > 0
, to the function
f
f
. These results involve comparisons between weighted
l
p
{l^p}
sums of the sequence
(
a
n
)
({a_n})
and weighted
L
p
{L^p}
integrals of
f
f
on
[
0
,
∞
)
[0,\infty )
.