Before revision: This paper concerns optimal error estimates for Legendre polynomial expansions of singular functions whose regularities are naturally characterised by a certain fractional Sobolev-type space introduced in 34, Math. Comput., 2019 . The regularity is quantified as the Riemann-Liouville (RL) fractional integration (of order 1-s\in (0,1)) of the highest possible integer-order derivative (of order m) of the underlying singular function that is of bounded variation.
After revision: This paper concerns optimal error estimates for Legendre polynomial expansions of singular functions whose regularities are naturally characterised by a certain fractional Sobolev-type space introduced in  . The regularity is quantified as the Riemann-Liouville (RL) fractional integration (of order 1-s\in (0,1)) of the highest possible integer-order derivative (of order m) of the underlying singular function that is of bounded variation.