de‧serv‧ed‧ly /dɪˈzɜːvədli, dɪˈzɜːvɪdli $ -ɜːr-/
adverb1. in a way that is right or deserved
deservedly popular/well-known/famous etc
Bistro Roti is a deservedly popular restaurant. Arsenal were deservedly beaten 2–1 by Leeds.2. (and) deservedly so used to say that you agree that something is right and deserved:
She is widely respected in the music world, and deservedly so. [TahlilGaran] Dictionary of Contemporary English ▲