In Katznelson's Introduction to harmonic Analysis there is a theorem which follows from a lemma on p. 64 chapter 3
Theorem: E is a Set of Divergence for B ( B is a homogenous Banach Space) if and only there exists an $ f \in B$ so that,
$$ S^*(f,t)= sup_n |S_n (f,t) | =\infty $$ for $ t \in E $
Lemma: Let be $ g \in B$. There exists an Element $f \in B $ and a positive, even sequence $ \{ \Omega_j \} $ with $ \lim_{j \rightarrow \infty} \Omega_j = \infty $ so that $ \hat{f}(j) = \Omega_j \hat{g}(j) $ for all $ j \in \mathbb{Z} $.
The Book says, the theorem is an easy consequence of the Lemma. I don't understand why. I would appreciate, if someone could explain it to me. Thank you in advance