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- W115485177 abstract "In this chapter we introduce and analyze an important class of Banach spaces consisting of functions, the so-called L p -spaces, where p is a parameter that specifies a particular space. First, in Section 5.1 we discuss some vector spaces and concepts that play a role in the analysis of the L p -spaces. In Section 5.2 we introduce the space L 1 ( $$mathbb R$$ ), and show how to make it a normed space. Integration techniques in L 1 ( $$mathbb R$$ ) are discussed in Section 5.3; in particular, we consider techniques for interchanging an integral and an infinite sum. For p∈]1,∞], the spaces L p ( $$mathbb R$$ ) are introduced in Section 5.4; their counterparts L p(a, b) concerning functions defined on a subinterval ]a, b[⊂ $$mathbb R$$ are discussed in Section 5.5." @default.
- W115485177 created "2016-06-24" @default.
- W115485177 creator A5017121787 @default.
- W115485177 date "2010-01-01" @default.
- W115485177 modified "2023-10-18" @default.
- W115485177 title "The L p -spaces" @default.
- W115485177 doi "https://doi.org/10.1007/978-0-8176-4980-7_5" @default.
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