I'm reading Nonlinear dispersive equations: local and global analysis by Terrance Tao and on page 335 he states the following theorem:
if $1 < p < q < \infty$ and $1/p < 1/q + s/d$ then
$$\| f \|_{L_x^q(\mathbb{R}^d)} \lesssim_{p, s, q, d} \| f \|_{W_x^{s,p}(\mathbb{R}^d)}.$$
As I understand this, this means that there is some constant, $C > 0$, which depends on $p, s, q, \text{ and } d$ such that
$$\| f \|_{L_x^q(\mathbb{R}^d)} \leq C \| f \|_{W_x^{s,p}(\mathbb{R}^d)}.$$
But, this seems trivial to me. The only variables in play are $p, s, q, \text{ and } d$ and the quantities $\| f \|_{L_x^q(\mathbb{R}^d)}$ and $\| f \|_{W_x^{s,p}(\mathbb{R}^d)}$ are just some real constants so, of course, one is less than a constant factor of the other. I suppose if the right hand side were zero and the left hand side were not, then this would say something more, but I suspect I'm just misunderstanding what the theorem is getting at.