Text this: Composition operators induced by monomial symbols and symbols with φ(D)⊂D

 _    _      ___      _____    _    _     ____    
| |  | ||   / _ \\   / ____|| | || | ||  |  _ \\  
| |/\| ||  | / \ || / //---`' | || | ||  | |_| || 
|  /\  ||  | \_/ || \ \\___   | \\_/ ||  | .  //  
|_// \_||   \___//   \_____||  \____//   |_|\_\\  
`-`   `-`   `---`     `----`    `---`    `-` --`