Hardy space
When 1 &lt; "p" &lt; ∞, "H(f)" belongs to "Lp"(T) when "f" ∈ "Lp"(T), hence the real Hardy space "Hp"(T) coincides with "Lp"(T) in this case. For "p" = 1, the real Hardy space "H"1(T) is a proper subspace of "L"1(T).