Demai, Chapter 4, Mishnah 2. This mishnah deals with a man who wants his friend to eat at his table so badly that he is prepared to take a vow forbidding him to derive any benefit from all his property if he will not eat with him. The difficulty is that the host is an am ha'aretz, whom the guest does not trust in matters of tithes. The Rishonim add an interesting layer: the mishnah is speaking of a young man marrying a young woman - a couple marrying for the first time, neither of whom had been married before - and for his sake an exceptional leniency is established here.
The ruling that emerges from the mishnah:
A man takes a vow against his friend that he must eat at his home, and if not, he will forbid him to benefit from all his property; but this man who is vowing is not trusted regarding tithes. And this is the distinction the mishnah draws:
"BaShabbos harishonah" - on the first Shabbos he is permitted to eat at his home, even though ordinarily he would not rely on him in matters of tithes, provided that the host tells him and assures him that the tithes have already been separated. In such a case we are lenient and rely on his word, even though in truth he is not trustworthy.
"BaShabbos hasheniyah" - if the matter repeats itself, then even though the one vowing carries out his threat and forbids him to benefit from his property, he may not eat until he tithes.
The reason for the difference: by the second week he had an opportunity to tithe the food in advance, or to speak to the host about tithing it beforehand - in other words, there was time to do something about it. On the first Shabbos, by contrast, it is possible that no opportunity for this presented itself at all.
This leniency of the first Shabbos, as noted in the words of the Rishonim, was stated with regard to the wedding feast of a young man marrying a young woman.