Lebesgue space L^0(D, dλ^2) | Lebesgue space L^2(D, dλ^2) | Lebesgue space L^∞(D, dλ^2)

space of measurable complex-valued functions on the disk

space of square-integrable complex-valued functions on the disk

space of essentially boundded complex-valued functions on the disk

The space of equivalence classes of equal-almost-everywhere complex-valued functions on the complex open unit disk

The space of equivalence classes of equal-almost-everywhere complex-valued functions which are square-integrable under two-dimensional normalized Lebesgue integration on the complex open unit disk D. More precisely, it is the space of equivalence classes of functions f from D to C for which the norm left double bracketing bar f right double bracketing bar _(L^2(D)) = sqrt( integral_D( left bracketing bar f(z) right bracketing bar )^2dλ^2) is finite. Implicitly, the space is equipped with the topology determined by this norm.

The space of equivalence classes of equal-almost-everywhere complex-valued functions on D which are essentially bounded with respect to normalized Lebesgue measure. More precisely, it is the space of equivalence classes of functions f from D to C for which the norm left double bracketing bar f right double bracketing bar _(L^∞(D)) = esssup_(z element D) left bracketing bar f(z) right bracketing bar is finite. Implicitly, the space is equipped with the topology determined by this norm.

Short notation: L^0 Alternate notations: L^0 | L_0 | S | L^0(D) Measure space: (D, dλ^2)

Short notation: L^∞ Alternate notations: L^∞ | L_∞ | L^∞(D) Measure space: (D, dλ^2) Norm: left double bracketing bar f right double bracketing bar _(L^∞(D, dλ^2)) = esssup_(z element D) abs(f(z))

Related spaces: L^∞(T;X) | L^ formal p (T;X) | ...

Related spaces: L^∞(T;X) | L^ formal p (T;X) | ...

Related spaces: L^∞(T;X) | L^ formal p (T;X) | ...

dual space | trivial space dual space map | F(f)(g) = 0 related results | Poincaré-Friedrichs inequalities

dual space | Lebesgue space L^2(D, dλ^2) related results | Banach-Saks theorem | Lax-Milgram theorem | Littlewood-Paley decomposition

pre-dual space | Lebesgue space L^1(D, dλ^2) related results | Poincaré-Friedrichs inequalities