Projects per year

## Personal profile

### Biography

**Educational background:**

B.A. 2000--2004 (Sun Yat-Sen University), Ph.D. 2004--2009 (Sun Yat-Sen University, Macquarie University, Cotutelle).

**Faculty position:**

Jan 2017---Present, Macquarie University, Senior Lecturer

Jan 2014--Dec 2016, Macquarie University, Lecturer

Jun 2012--Jan 2014, Sun Yat-Sen University, Associate Professor

Aug 2009--May 2012, Sun Yat-Sen University, Lecturer

**Research Grants:**

1. The ARC Discovery Project, Grant No. DP170101060, 2017--2019, Chief Investigator (with A/Prof. Zihua Guo (CI), Prof. Carlos Kenig (PI) , Prof. Kenji Nakanishi (PI).

2. The ARC Discovery Project, Grant No. DP160100153, 2016--2018, Chief Investigator (with Prof. Xuan Duong (CI), A/Prof. Lesley Ward (CI) , Prof. Michael Lacey (PI), Prof. Jill Pipher (PI)).

3. Macquarie University Research Seeding Grant, 2018--2019.

4. Macquarie University New Staff Grants Scheme (MQNS), 2016.

5. The NNSF of China, Grant No. 11001275, 2011--2013, Sole investigator.

6. China Postdoctoral Science Foundation funded project, Grant No. 201104383, 2011--2013, Sole investigator.

7. The Fundamental Research Funds for the Central Universities, Grant No. 11lgpy56, 2011--2013, Sole investigator.

**Research impact:**

1. At this phase of my career, I have 275 citations by 175 authors listed in MathSciNet (as of June 2019).

2. Among all my publications, some of the papers are published in

- Memoirs of the American Mathematical Society,
- Journal de Mathematiques Pures et Appliquees,
- Annales de l'Institut Fourier,
- Indiana University Mathematics Journal,
- Mathematische Zeitschrift,
- Transaction of the American Mathematical Society.

These journals have long tradition and reputation in the world.

Also, some other papers are published in

- Analysis and PDE,
- Applied and Computational Harmonic Analysis,
- Journal d'Analyse Math\'ematique,
- Journal of Functional analysis,
- Journal of Differential Equations, and
- Revista Matem\'atica Iberoamericana.

These are top international journals in the field of analysis.

3. One of my paper published in Journal of Functional Analysis is one of the ``most cited articles since 2011'' of this journal.

It is cited 50 times up to 2019 as listed in MathSciNet.

4. Two of my papers have been cited by Professor E. Stein (Wolf prize 1999, Steele Prize 1984 and 2002, Schock Proze 1993, one of the most influential mathematicians in the past 40 year) in his recent paper (Memo. Amer. Math. Soc. 2018,\ \ http://arxiv.org/abs/1511.05702).

5. I have been invited to give a talk in the Satellite Conference in Harmonic Analysis, in ICM 2018, Brazil.

** **

**Papers accepted for publication:**

1. Y. Han, M.Y. Lee, J. Li and B.D. Wick, Maximal function, Littlewood-Paley theory, Riesz transform and atomic decomposition in the multi.parameter flag setting, accepted in Apr 2019 by Memoirs of the American Mathematical Society.

2. J. Li, T. Nguyen, L.A. Ward and B.D. Wick, The Cauchy Integral, bounded and compact commutators, accepted in Nov 2018 by Studia Math.

3. T.A. Bui, X. Duong, J. Li, and B.D. Wick, Functional calculus of operators with heat kernel bounds on non-doubling manifolds with ends, accepted in Nov 2018 by Indiana University Mathematics Journal.

4. Z. He, Y. Han, J. Li, L. Liu, D. Yang and W. Yuan, A complete real-variable theory of Hardy spaces on spaces of homogeneous type, accepted in Oct 2018 by J. Fourier Anal. Appl.

5. J. Li, R. Rahm and B.D. Wick, A_p weights and quantitative estimates in the Schr\"odinger setting, accepted in Oct 2018 by Math. Z.

6. Y. Han, J. Li, C.-C. Lin and C. Tan, A class of singular integrals associated with Zygmund dilations, accepted in Aug 2018 by Journal of Geometric Analysis.

7. Y.C. Han, Y.S. Han, J. Li and C. Tan, Marcinkiewicz multipliers and Lipschitz spaces on Heisenberg groups, accepted in Feb 2018 by Canadian Journal of Mathematics.

** **

**Service:**

1. Colloquium Convenor, Department of Mathematics (2016--2017)

http://www.mq.edu.au/about/about-the-university/faculties-and-departments/faculty-of-science-and-engineering/departments-and-centres/department-of-mathematics/news-and-events/Colloquium

2. Main organiser of the international workshop ``Harmonic analysis and PDE'' in Macquarie University in 17--21, July 2017.

http://www.mq.edu.au/about/about-the-university/faculties-and-departments/faculty-of-science-and-engineering/departments-and-centres/department-of-mathematics/news-and-events/2017-harmonic-analysis-and-pde-workshop

3. Member of the local organising committee, Organiser of the Harmonic Analysis Session of 61st Annual Meeting of the Australian Mathematical Society, 12--15 Dec, 2017, at Macquarie University.

4. Co-organizer of the joint seminar “Analysis and PDE meeting”:

This is a joint seminar begins from 2014, first named ``WOMASY--Geometric and Harmonic Analysis meets PDE'', among the geometric analysis group at the University of Wollongong, the harmonic analysis group at Macquarie UNIVERSITY AND the nonlinear analysis group at the University of Sydney:

(1). 1st October 2014 at University of Sydney. http://www.maths.usyd.edu.au/u/PDESeminar/womasy/index-2014-10.html

(2). 17th February 2015 at Macquarie University. http://www.maths.usyd.edu.au/u/PDESeminar/womasy/

From July 2015, the joint seminar ``WOMASY--Geometric and Harmonic Analysis meets PDE'' has changed as ``Analysis and PDE meeting''. I continue to serve as a Co-organiser of this joint seminar ``Analysis and PDE meeting'': joint with University of Wollongong, MAcquarie University, The University of Sydney, UNSW, ANU, University of New Castle.

(3). Monday 20 July 2015 at University of Wollongong. http://www.maths.usyd.edu.au/u/PDESeminar/analysis-and-pde/2015/07/

(4). 10 Feb 2016 at ANU. http://www.maths.usyd.edu.au/u/PDESeminar/analysis-and-pde/2016/02/

(5). 19th Jul 2016 at UNSW. http://www.maths.usyd.edu.au/u/PDESeminar/analysis-and-pde/2016/07/

### Research interests

**Areas of specialization and related research interests:**

The area of my specialization is Harmonic Analysis, especially the following topics:

1. Singular integrals and function classes in the multi-parameter setting;

2. Singular integrals, multilinear singular integrals with non-smooth kernels, and function classes associated with operators;

3. Dyadic structures, weighted norm inequalities, and related problems;

4. Singular integrals and function classes on domains with non-doubling measures.

### Education/Academic qualification

Pure Math, PhD (Cotutelle), Macquarie University

1 Aug 2008 → 30 Nov 2009

Pure Math, PhD, Sun Yat-Sen University

1 Sep 2004 → 30 Jun 2009

## Fingerprint Dive into the research topics where Ji Li is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

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## Projects 2016 2022

## Harmonic analysis and dispersive partial differential equations

Li, J., Guo, Z., Kenig, C. & Nakanishi, K.

31/01/17 → …

Project: Research

## Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals

Duong, X., Ward, L., Li, J., Lacey, M., Pipher, J. & MQRES, M.

16/02/16 → …

Project: Research

## Harmonic analysis, complex analysis and differential operators

Duong, X., Li, J., Ward, L., Lacey, M., Pipher, J. & Wick, B.

1/01/20 → 31/12/22

Project: Research

## Research Outputs 2009 2019

## Lower bound of Riesz transform kernels and commutator theorems on stratified nilpotent Lie groups

Duong, X. T., Li, H-Q., Li, J. & Wick, B. D., Apr 2019, In : Journal des Mathematiques Pures et Appliquees. 124, p. 273-299 27 p.Research output: Contribution to journal › Article › Research › peer-review

## Commutators of multiparameter flag singular integrals and applications

Duong, X. T., Li, J., Ou, Y., Pipher, J. & Wick, B. D., 1 Jan 2019, In : Analysis and PDE. 12, 5, p. 1325-1355 31 p.Research output: Contribution to journal › Article › Research › peer-review

## Haar bases on quasi-metric measure spaces, and dyadic structure theorems for function spaces on product spaces of homogeneous type

Kairema, A., Li, J., Pereyra, M. C. & Ward, L. A., 1 Oct 2016, In : Journal of Functional Analysis. 271, 7, p. 1793-1843 51 p.Research output: Contribution to journal › Article › Research › peer-review

## Hardy space theory on spaces of homogeneous type via orthonormal wavelet bases

Han, Y., Li, J. & Ward, L. A., Jul 2018, In : Applied and Computational Harmonic Analysis. 45, 1, p. 120-169 50 p.Research output: Contribution to journal › Article › Research › peer-review

## A complete real-variable theory of Hardy spaces on spaces of homogeneous type

He, Z., Han, Y., Li, J., Liu, L., Yang, D. & Yuan, W., Oct 2019, In : Journal of Fourier Analysis and Applications. 25, 5, p. 2197-2267 71 p.Research output: Contribution to journal › Article › Research › peer-review