in the next week, on the next week都可以。
in the next week 在下一周
in the last week 在上一周
注:因为有定冠词the,是指你说话语境时间的上下周。
What will you do in the next week?
下周你将做什么?
is on the next week和is next week含义和用法上的差别,第一个意为在下周,第二个意为是下周。
例句:What is on TV next week in chinese?
下星期在中国的电视上是什么?