Complex sentence: Epstein was asked to appear on several music-based TV programmes in Britain after the success of The Beatles, and also hosted a regular part of the US TV show "Hullabaloo", by filming his appearances in the UK.
Split into simpler sentences: Epstein was asked to appear on several music-based TV programmes in Britain after the success of The Beatles. He also hosted a regular part of the US TV show "Hullabaloo", filming his appearances in the UK.