Complex sentence: He was born in Rome, where he studied under Cortona, and for whom he completed fresco paintings of the ceilings and other internal decorations begun by his instructor in the Pitti Palace, Florence.
Split into simpler sentences: He was born in Rome, where he began working under Cortona. He followed Cortona and completed for him the frescoed ceilings and other internal decorations begun in the Pitti Palace, Florence.