A cell phone sends radio signals and thereby emits electromagnetic radiation.
Although the word "radiation" has become very scary, that is nothing evil in itself. The dangers with radiation depend very much on the "hardness" of the radiation and of course on the intensity. "Hardness" depends on wavelength.
"Radio"-waves as used by a cellphone are very "soft" radiation. Harder are microwaves. Harder still visible light! Beyond visible light, ultraviolet, x-rays and gamma-rays are becoming ever more dangerous. Gamma rays constitute a large part of what is known as "radio-active radiation" from e.g. nuclear weapons.
Regarding the intensity, the legal norms for cellphones set the limit at quite low figures, considerably less than those of any light-bulb.
A cellphone therefore emits radiation that is both softer than and of less intensity than a lightbulb! Until today, no scientifically solid evidence of any dangers posed by cellphone radiation have been found, although many have searched for such evidence.
The issue with an elevator is, that is can be seen as a metal box. Metal walls reflect radiation back. Under "perfect" circumstances, this could lead to an enormous buildup of radiation within such a box (always limited by the time you are inside the elevator and the energy that a small cellphone accu can deliver).
In practice, the circumstances inside an elevator are far from "perfect". I cannot go into the details of the physics here, but imperfect conductivity of the walls plays a role as well as the presence of further absorbing "material" within the elevator. Again, the lighting in the elevator does not build up to high levels either.
In consideration of the above, I have never hesitated to use a cell phone within an elevator.