Assuming the item has the value "asd", your main list will always be two levels deep, as in your example, and your returned result should be in the same format, this should happen.
List1 = [["asd", "ddsa"], ["ASD", "ASD"], ["FH", "SDFDF]]
[ [ F(String) || String <- List2 ] || List2 <- List1 ]
If you mean that your element ["asd", "ddsa"] just uses lists: map / 2 or a list comprehension, as shown below.
List1 = [["asd", "ddsa"], ["ASD", "ASD"], ["FH", "SDFDF]]
[ F(List2) || List2 <- List1 ]
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