From http://www.mayoclinic.com/health/asthma/AN00443
Answer from James T. Li, M.D.
Despite manufacturers' claims, ozone air purifiers don't remove asthma triggers from the air. In fact, inhaled ozone can make asthma worse.
Inhaling ozone, even in small amounts, can irritate the lungs. Specific effects may include throat irritation, coughing, chest pain and shortness of breath, as well as an increased risk of respiratory infections.
Another good source is http://www.epa.gov/apti/ozonehealth/effects.html - it has too many points of interest to cite, so I picked one study at random:
. Use of inhaled beta-adrenergic agonist medication to alleviate asthma aggravation is plotted against ozone concentrations during summer asthma camps conducted for children 7 to 13 years old, during the last week of June, 1991 through 1993, in the Connecticut River Valley, downwind of New York City. Each child's normal physician-prescribed medications were maintained throughout each week. An increase in the 1-hour daily maximal ozone concentration from 84 to 160 ppb was significantly associated with increased unscheduled medications administered per day. Source: Thurston et al., 1997