#lorentz space

[mathkonspekt]

Lorentz spaces

[mathkonspekt]

Lorentz space

What are Lorentz spaces $L_{pq}$? Shortly speaking, they are generalizations of Lebesgue spaces $L_p$, and were introduced by George Lorentz in 1950.

Here I will collect books and sources which would help to learn about Lorentz spaces (no doubt the wikipedia is the first step). 1. Introduction to Fourier analysis on Euclidean spaces by Elias Stein & Guido Weiss. See chapter V section 3, where authors start with distribution function and nonincreasing rearrangement and then define $L_{pq}$ space. 2. Terence Tao notes for 247A is also good starting point to learn Lorentz spaces. Also 247A Notes on Lorentz spaces.

3. Another big book is Classical Fourier Analysis by Loukas Grafakos. 4. Introduction to Lorentz spaces (which I believe is a diploma paper) seems to contain comprehensive introduction from functional analysis point of view. Another master thesis on the topic  Decreasing  Rearrangement  and Lorentz $L(p, q)$ Spaces by Erik Kristiansson.

to be continued...