Complex sentence: He returned to California and in the 1940s and 1950s his band was an important force in reviving interest in New Orleans style jazz, making popular radio broadcasts (including on the Orson Welles show) and recordings.
Split into simpler sentences: He returned to California and in the 1940s and 1950s. His band was an important force in reviving interest in New Orleans style jazz, making popular radio broadcasts (including on the Orson Welles show) and recordings.