As I was reading HARDY SPACES $H^p$, It's definition clearly states that it is the space of analytic functions on a unit disc satisfying norm conditions.
I didn't get that ,the texts say that $H^p$ is a subset of $L^p$ , How is that even possible because $L^p$ is a collection of equivalence classes.
Kindly help! Thanx n regards
The author is abusing notation a bit. Given any $H^p$ function $F: \mathbb{D} \to \mathbb{C}$, you can look at the associated boundary value function $f : S^1 \to \mathbb{C}$ given by $f(\zeta) = \lim_{z \to \zeta} F(z)$ where the limit here is taken non-tangentially (I'm sure your book discusses this). The point is that this $f$ is in $L^p$, and the association $F \mapsto f$ is injective. So, we can basically view $H^p$ as a subset of $L^p$.