Ozone (O3) high in the atmosphere absorbs ultraviolet radiation from the sun, thereby protecting living organisms below from this dangerous radiation. The term ‘ozone hole’ refers to recent depletion of this protective layer over Earth's polar regions. People, plants, and animals living under the ozone hole are harmed by the solar radiation now reaching the Earth's surface—where it causes health problems from eye damage to skin cancer.
The ozone hole, however, is not the mechanism of global warming. Ultraviolet radiation represents less than one percent of the energy from the sun—not enough to be the cause of the excess heat from human activities. Global warming is caused primarily from putting too much carbon into the atmosphere when coal, gas, and oil are burned to generate electricity or to run our cars. These gases spread around the planet like a blanket, capturing the solar heat that would otherwise be radiated out into space. (For more detail on the basic mechanism of global warming, see carbon dioxide FAQ.)
Both of these environmental problems do, however, have a common cause—human activities that release gases into and alter the atmosphere. Ozone depletion occurs when chlorofluorocarbons (CFCs)—formerly found in aerosol spray cans and refrigerants—are released into the atmosphere. These gases, through several chemical reactions, cause the ozone molecules to break down, reducing ozone's ultraviolet (UV) radiation-absorbing capacity.
Because our atmosphere is one connected system, it is not surprising that ozone depletion and global warming are related in other ways. For example, evidence suggests that climate change may contribute to thinning of the protective ozone layer.
I quote the above from the below article:
http://www.ucsusa.org/global_warming/science_and_impacts/science/ozone-hole-and-gw-faq.html
This should help to answer your question in a very scientific manor.