Ozone protects us by absorbing ultraviolet radiation
As shown in this Chemistry.SE answer, ozone breaks upon incidence of various energies of UV radiation to form oxygen, which itself is somewhat effective at blocking UV radiation at other energies. THe key is that the incident UV radiation transfers its energy to the reaction products in order to break the bonds holding ozone (or oxygen) together.
As opposed to protecting us from UV, the only way for ozone to protect us from global warming is for it to reflect the incident UV radiation back into space. That is not what it does. UV that enters the Earth's atmosphere and interacts with the ozone stays in the Earth's atmosphere.
Therefore, your question premise is flawed when you say "if ozone layers gets smaller, more UV radiation enters on Earth." That is not true, because UV radiation that that enters the Earth will be absorbed by something, whether it is ozone or the rest of the atmosphere or the ground.
Global warming deals with infrared radiation
Furthermore, 'global warming' is primarily concerned with radiation heading outwards in the infrared band. IR radiation emitted from the ground is blocked by CO$_2$ in the atmosphere and prevented from escaping into space. So the effect of ozone on UV radiation will have little to no effect on 'global warming'.