It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

# Theory of Function Spaces: Course Outline (MAT-621)

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.

## Course Outline

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.