Are $L^{p}$ spaces a part of Functional Analysis?

I recently tagged this question as functional analysis in addition to measure theory and $L^{p}$ spaces. However, I was not completely sure whether functional analysis is an appropriate tag for $L^{p}$ spaces. After some thought, I left the tag so that the question receives more attention.

Is it correct to tag question about $L^{p}$ as functional analysis specially when we have a dedicated tag for $L^{p}$?

• Well the functional analysis course I am taking now certainly has the topic "$L^p$ spaces" included....
– user38268
Aug 31 '13 at 12:02

1 Answer

Yes, is a perfectly acceptable tag for questions about $L^p$ spaces in general, and for that question in particular. The existence of a specific tag doesn't make a more general one inappropriate.

• So is it true that functional analysts are likely to be well versed with $L^{p}$ spaces? Aug 31 '13 at 5:12
• @Vishal: I would say so. But then again, they're a sufficiently fundamental part of analysis that I think almost any analyst will be well versed in them. Aug 31 '13 at 5:20
• Yeah probably true. Aug 31 '13 at 5:45
• @Vishal Especially the $L^p$ spaces as foundation for the Lorentz and Sobolev spaces are important in functional analysis. It's like matrices for linear algebra I guess... Sep 8 '13 at 19:51
• @AlexR I did not know that $L^{p}$ is to functional analysis what matrices is to Linear Algebra. I always thought $L^{p}$ being a measure theory topic; especially the techniques. Sep 9 '13 at 4:07