Hardy space
When 1 ≤ "p" &lt; ∞, the "real Hardy spaces" "Hp" discussed further down in this article are easy to describe in the present context. A real function "f" on the unit circle belongs to the real Hardy space "Hp"(T) if it is the real part of a function in "Hp"(T), and a complex function "f" belongs to the real Hardy space iff Re("f") and Im("f") belong to the space (see the section on real Hardy spaces below). Thus for 1 ≤ "p" &lt; ∞, the real Hardy space contains the Hardy space, but is much bigger, since no relationship is imposed between the real and imaginary part of the function.