Hardy space
If 1 &lt; "p" &lt; ∞, the Hardy space "Hp" is the same vector space as "Lp", with equivalent norm. When "p" = 1, the Hardy space "H"1 is a proper subspace of "L"1. One can find sequences in "H"1 that are bounded in "L"1 but unbounded in "H"1, for example on the line