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To invite a visitor to one's house (especially if the visitor must travel north to get there). My cousins in Pennsylvania have asked me up to their house for the weekend, but that's a long drive from Florida.
ask someone up
to ask someone to come to one's home for a visit. (Usually said when someone must travel north, up a hill, or to an apartment on a higher floor for the visit.) Let's ask Judy up for the weekend. We asked up a few old friends.