Is fasting on Sundays prohibited by some Church law or is it just not recommended generally?
The reason fasting on Sundays is not usually done is that fasting is generally considered a penitential exercise, and penitential exercises are normally lifted on a solemnity (which Sunday always is). This is why every Lent many people ask if whatever they gave up for Lent can be partaken of on the Sundays of Lent. Each Sunday is also a miniature celebration of Easter Sunday, which therefore is considered a day of celebration and rejoicing rather than penance.
However, that being said, personal spiritual fasting is not prohibited on Sundays. Catholics are free to fast in various ways in their personal spiritual journey, though it is recommended that they do so in consultation with a spiritual director.