Is there a name for embedding of Lebesgue spaces $L^q(a,b) ⊂ L^p(a,b)$

Question

Let $1 ≤ p ≤ q ≤ ∞$

then

$L^q(a,b) ⊂ L^p(a,b)$

where $L^q(a,b), L^p(a,b)$ are Lebesgue spaces

Is there a name for this relationship? Is this the Sobolev embedding theorem?

Answer 1

The embedding does not have a standard name. For example, no particular name is used in the article Another Note on the Inclusion $L^p(μ)⊂L^q(μ)$ which is entirely about this fact.

Some of the ways to refer to it:

• since the Lebesgue spaces are nested...
• by the nested property of the Lebesgue spaces...
• the inclusion between Lebesgue spaces...
• by Jensen's inequality/Hölder's inequality (suggested by PhoemueX)