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

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Lokenath Debnath and Piotr Mikusinski. Introduction to Hilbert Spaces with Applications, 2nd ed. 1999. Dragiša Mitrović and Darko Žubrinić. Fundamentals of Applied Functional Analysis. 1998. Thomas Runst and Winfried Sickel. Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. 1996. Terence Tao. "A Type Diagram for Function Spaces." 2010. https://terrytao.wordpress.com/2010/03/11/a-type-diagram-for-function-spaces/. Hans Triebel. Theory of Function Spaces. 2010. Wen Yuan, Winfried Sickel, and Dachun Yang. Morrey and Campanato Meet Besov, Lizorkin and Triebel. 2010.