Viking traders were operating in the Black Sea. The Byzantine Emperors' "Varyngian" bodyguards were probably Norsemen. Also, the Norse conquered and ruled Sicily for a time. They were operating a LONG way from home waters.
"Also, the Norse conquered and ruled Sicily for a time."
More than Sicily. The leader was a relative (cousin, brother?) of William the Conqueror (France, England, 1066...that thing).
Bari, Italy was their capital, and they controlled a significant amount of territory, including the Holy Lands.