Originally the lulav was taken in the Temple seven [days], and in the provinces [it was taken] one day.  After the Temple was destroyed, Rabban Yochanan ben Zakkai instituted that the lulav be taken in the provinces seven [days] in remembrance of the Temple; and that the entire Day of Waving be forbidden.

On the first day of the Festival that fell on the Sabbath, all the people would bring their lulavim to the synagogue. On the morrow they would awaken early and come. Everyone would recognize his own [lulav] and take it, for the Sages said: A man cannot fulfill his obligation on the first day of Succos with a lulav belonging to his friend; but on the other days of Succos a man can fulfill his obligation with a lulav belonging to his friend.

R’ Yose says: If the first day of Succos fell on the Sabbath, and one forgot and carried the lulav out into the public domain, he is exempt —- for he carried it out with permission.

15. A woman may accept [a lulav] from her son or from her husband and return it to the water on the Sabbath.  R’ Yehudah says: On the Sabbath we return [it], on the Festival we add [water], and during [the Intermediate Days of] the Festival we change [the water].  A minor who knows how to wave is obligated to take the lulav.