Operators on Sobolev Type Spaces (Communications in Mathematical Research, 2023)
In this paper, we introduce the work done on Hardy-Sobolev spacesand Fock-Sobolev spaces and their operators and operator algebras, including the study of boundedness, compactness, Fredholm property, index theory,spectrum and essential spectrum, norm and essential norm, Schatten-p classes,and the $C^∗$ algebras generated by them.
Keywords: Hardy-Sobolev space; Fock-Sobolev space; multiplier; composition operator; Toeplitz operator; Hankel operator.