What did henry hudson claim land for

Henry Hudson never claimed US land for the Dutch. There was no New Jersey and no New York.

In 1609 Henry Hudson was working for the Dutch East India Company, not the government of the Netherlands.

The purpose of Hudson's voyages was to find a shorter route (the theoretical Northwest Passage) to the East Indies for the purpose of trade.

He claimed land most of Canada (he found some parts of Canada) and he also found some on Iceland. He would use them for land (like houses)