An integral formula for Schatten norm on the Hardy space: The only high-dimensional case

In [8], an exact integral formula was proved for the Schatten p-norm of Hankel operators on the one-variable Hardy space for p = 2, 4, and 6. Moreover, it was shown that these are the only values of p for which such a formula is possible. It was further pointed out in [8] that the only possibility for a meaningful multi-variable analogue of this formula is the case where n = 2 and p = 6. We show that the conjectured integral formula indeed holds in this one possible multi-variable case. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The paper proved an exact integral formula for the Schatten p-norm of Hankel operators on the one-variable Hardy space for p = 2, 4, and 6. It was also shown that these are the only values of p for which such a formula is possible. Furthermore, it was pointed out that the only meaningful multi-variable analogue of this formula is when n = 2 and p = 6.