Meaning of $L^p$, $1\leq p < \infty$

Question

What does "$L^p$, $1\leq p < \infty$" mean? For a finite $p\geq 1$ (e.g. $p=1$ or $p=3$)? Or for all finite $p\geq 1$?

P.S. I understand what $L^p$ means, I just have problems understanding the part about the values of $p$.

To the downvoter: This is a genuine question. I do not understand the notation and there is a tag for this. — Combo, Nov 03 '14 at 23:58
In general, you are looking at $L^p$ for a specific fixed $p$. — Joel, Nov 04 '14 at 00:02

score 2 · Accepted Answer · answered Nov 04 '14 at 00:02

2

This notation typically refers to some $L^p$ space where $p$ is a fixed but unspecified value over the given range, i.e., $p$ is an arbitrary, fixed, finite value greater than or equal to one.

answered Nov 04 '14 at 00:02

yoknapatawpha

4,009

Many thanks for the clarification. – Combo Nov 04 '14 at 00:03
Happy to help. If you found this or the other answer(s) helpful, you might consider upvoting them and accepting whichever you found most helpful. – yoknapatawpha Nov 04 '14 at 00:06
Sure, I just need to wait for another 4 minutes. – Combo Nov 04 '14 at 00:06

Meaning of $L^p$, $1\leq p < \infty$

1 Answers1