It says "con sordina", which means "with mute" or "with damper" so I think that means don't depress the pedal as that would remove the dampers which would be written as "senza sordina". At least, that is the reason Andras Schiff used in one of his Beethoven lectures for using the pedal in the moonlight sonata, which says "senza sordini" (without dampers).