A function space is a topological space whose points are functions. There are many different kinds of function spaces, and there are usually several different topologies that can be placed on a given set of functions.

**Vector and norm spaces**

**Lebesgue sequence and function spaces**: Lebesgue sequence spaces and related theorems. Hardy and Hilbert inequalities. Essentialy bounded functions, Lebesgue spaces (p>1), Embeddings, Approximation in Lebesgue spaces, Duality, Reflexivity, weak convergence and continuity of translation operator, weighted Lebesgue spaces, Isometries, Lebesgue spaces (0<p<1).

**Distribution Function and Rearangements: **Distribution functions, Decreasing Rearangements, Rearanagement of Fourier Transform.

**Weak Lebesgue spaces: **Weak Lebesgue spaces, Convergence in Measure, Interpolation and Normability.

**Lorentz Spaces: **Lorentz space and Normability, Completeness, Separbility, Duality, Lorentz sequence spaces.

**Non-Standard Function spaces: **Variable Lebesgue space Definition and their properties. Some differences between constant exponent and variable exponent spaces. Grand Lebesgue space, Amalgam and Herz type spaces with variable exponents.

- An Introductory Course in Lebesgue Spaces byCall Number: 515.785 CASISBN: 9783319300320Publication Date: 2016-07-06

- Function Spaces, 1 : Volume 1 by Luboš Pick, Oldrich John, and Svatopluk FucíkISBN: 9783110250428

Publication date: 2013-01-01

- Optimization in Vector Spaces byCall Number: 515.73 SASISBN: 9780486789453Publication Date: 2016-03-15

- Narrow Operators on Function Spaces and Vector Lattices by Mikhail Popov, Beata Randrianantoanina, and Carsten CarstensenISBN 9783110263343

Publication date: 2012-12-06 - Optimal Domain and Integral Extension of Operators : Acting in Function Spaces by S. Okada, Werner J. Ricker, and Enrique A. Sanchez PerezISBN 9783764386481

Publication date: 2008-09-30 - Topology with Applications : Topological Spaces Via near and Far by Somashekhar A. Naimpally and James F. PetersISBN 9789814407663

Publication date: 2013-02-21 - Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsing and Randall EubankISBN 9781118762561

Publication date: 2015-03-16 - Functional Equations and Inequalities in Several Variables by Stefan CzerwikISBN 9789812778116

Publication date: 2002-05-14