It could be the same fungus that afflicted my ghost peppers last summer. Without magnification, it looked like black stains and spatters of black ink on the leaves... by the way, that's a wonderful picture!
Our maritime climate (cool and often damp, every night, all summer) encourages many fungal diseases. A local tree, called 'wild crabapple' (Malus fusca) is a carrier for the black-spot disease of roses, called anthracnose.
The treatment i used was Listerine brand mouthwash, diluted 50% with water, sprayed on leaves (including undersides), as treatment and preventive, once a week. It worked for my ghost peppers too. The active ingredients, menthol and thymol, are safer on a food crop than any other fungicide i know of.
If that product is not available in Norway, locally available fungal treatments from your garden center may be best.
There may be some confusion of names here, as i believe another fungus species causes a disease of peppers that is also named 'anthracnose'.