We study the compactness of finite sums of products of two Toeplitz operators on Hardy–Sobolev spaces over the unit polydisk . We calculate the essential norm of these operators and answer the question of when a Toeplitz operator on is Fredholm.
"Compact Toeplitz operators products on Hardy–Sobolev spaces over the unit polydisk." Rocky Mountain J. Math. 51 (2) 549 - 570, April 2021. https://doi.org/10.1216/rmj.2021.51.549