Palestrina was alive 3 February 1525 or 2 February 1526 - 2 February 1594 so in the Italian Renaissance. He has often been seen in Renaissance polyphony. That's all I know.
He lived and worked during the time period of the Renaissance.
Vivaldi
20th Century ... and it's not past tense ... he is still living and currently composing.
Desprez and Palestrina.
Bach
PLAYED
Vivaldi
baroque
Mostly in the Romantic Era.
Motzart composed in the classical period. He actually taught Beethoven.
20th Century (American Folk Music)
20th Century ... and it's not past tense ... he is still living and currently composing.
Palestrina (Apex)
Desprez and Palestrina.
That would be Renaissance music. Specifically, Palestrina was a pioneer of the "Counter-Point" style of polyphonic choir music in the mid 1500's Italian Renaissance. Please correct me if I'm wrong, I've only sung his music in church choir, I have not studied it.
Bach
Baroque
Baroque period