ABSTRACT
In this chapter we examine the properties of spaces of measurable functions f for which | f | p $ |f|^p $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315151601/40b40f18-f94e-4633-83f0-b519efc5b015/content/inline-math4_2.tif"/> ( p > 0 ) $ (p>0) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315151601/40b40f18-f94e-4633-83f0-b519efc5b015/content/inline-math4_3.tif"/> is integrable, the so-called L p $ L^p $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315151601/40b40f18-f94e-4633-83f0-b519efc5b015/content/inline-math4_4.tif"/> spaces. These are among the most important examples of Banach spaces. In particular, the case p = 2 $ p = 2 $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315151601/40b40f18-f94e-4633-83f0-b519efc5b015/content/inline-math4_5.tif"/> is of critical importance in Fourier analysis.
