Research Publications:

  1. Geometric Arveson-Douglas conjecture for the Hardy space and a related compactness criterion. (with Jingbo Xia). Adv. Math. 388 (2021), Paper No. 107890, 54 pp. [pdf]

  2. The Helton-Howe trace formula for submodules. (with Quanlei Fang and Jingbo Xia), J. Funct. Anal. 281(2021), no. 1, 108997. [pdf]

  3. Essential commutants on strongly pseudo-convex domains. (with Jingbo Xia), J. Funct. Anal. 280(2021), no. 1, 108775, 56 pp. [pdf]

  4. Essential normality of principal submodules of the Hardy module on a strongly pseudo-convex domain. (with Jingbo Xia), J. Operator Theory 83(2020), no. 2, 333-352. [pdf]

  5. Toeplitz operators associated with measures and the Dixmier trace on the Hardy space. (with Liangying Jiang and Jingbo Xia), Complex Anal. Oper. Theory 14 (2020), no. 2, Paper No. 30, 58 pp. [pdf]

  6. Essential normality for quotient modules and complex dimensions. (with Jingbo Xia), J. Funct. Anal. 276 (2019), 1061-1096. [pdf]

  7. Essential normality - a unified approach in terms of local decompositions. Proc. Lond. Math. Soc. (3) 119 (2019), no. 5, 13881429. [pdf]

  8. Geometric Arveson-Douglas conjecture - decomposition of varieties. (with Ronald G. Douglas), Complex Anal. Oper. Theory 12 (2018), no. 5, 12671290. [pdf]

  9. Geometric Arveson-Douglas conjecture and holomorphic extension, (with Ronald G. Douglas), Indiana Univ. Math. J. 66 (2017), no. 5, 1499–1535. [pdf]

Preprints:

  1. On the p-essential normality of principal submodules of the Bergman modules on strongly pseudoconvex domains. (with Ronald G. Douglas and Kunyu Guo). submitted. [arXiv]

  2. A sharp inequality of Hardy-Littlewood type via derivatives. (with Hui Dan and Kunyu Guo). [arXiv]

  3. Helton-Howe trace, the Connes-Chern character and quantization (with Xiang Tang and Dechao Zheng). [arXiv]

  4. Trace invariants associated with quotient modules of the Hardy module . (with Jingbo Xia). submitted. [preprint]

Survey papers:

A survey on the Arveson-Douglas Conjecture. (with Kunyu Guo). In: Curto R.E., Helton W., Lin H., Tang X., Yang R., Yu G. (eds) Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology. Operator Theory: Advances and Applications, vol 278. Birkhäuser, Cham. [pdf]