Addendum to “The Lebesgue summability of trigonometric integrals” [J. Math. Anal. Appl. 390 (2012) 188–196]

We observed that statement (2.9) in Theorem 2 remains valid if condition (2.7) is replaced by the weaker condition that (2.7′) f ( t ) ∈ L 1 ( − T , T ) for all T > 0 .