Hi, I'm Abhishek Ghosh.

Currently, I am an Assistant Professor at the Department of Mathematics, Indian Institute of Technology Madras. Prior to that, I was a postdoctoral fellow at the Institute of Mathematics of the Polish Academy of Sciences, Warsaw. I completed my PhD from the Department of Mathematics, Indian Institute of Technology Kanpur under the supervision of Prof. Parasar Mohanty. The title of my PhD thesis is "New weighted inequalities for One-sided maximal function and multilinear Calderón-Zygmund operators." My research interest lies in harmonic analysis and partial differential equations.

email: abhi170791[AT]gmail.com; abhi[AT]iitm.ac.in, replace [AT] by @.

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Research Interest

Classical harmonic analysis related to maximal functions, singular integrals, pseudo-differential operators, and their weighted analogues.
Unique continuation problems and regularity theory of PDEs.

Selected Publications:

1. Spherical maximal functions and Hardy spaces for Fourier integral operators.

(with N. Liu, J. Rozendaal, L. Song)

J Geom Anal 36, 250 (2026).

Paper

1. Dimension free estimates for the vector-valued Hardy–Littlewood maximal function on the Heisenberg group.

(with P. Ganguly)

Journal of Functional Analysis, 290 (2026), no. 5, 111285, ISSN 0022-1236.

Paper

1. Sharp asymptotic of solutions to some nonlocal parabolic equations.

(with A. Banerjee)

Discrete Contin. Dyn. Syst. 45 (2025), no. 4, 1297–1334.

Paper

1. Decay at infinity for solutions to some fractional parabolic equations.

(with A. Banerjee)

Proc. Roy. Soc. Edinburgh Sect. A 155 (2025), no. 6, 1961–1997.

Paper

1. Sparse bounds for pseudo-multipliers associated to Grushin operators, II.

(with S. Bagchi, R. Basak & R. Garg)

J Geom Anal 34, 34 (2024).

Paper

1. Strong unique continuation for variable coefficient parabolic operators with Hardy type potential.

(with A. Banerjee & P. Ganguly)

J. Differential Equations 380 (2024), 92-145.

Paper

1. Sparse bounds for pseudo-multipliers associated to Grushin operators, I.

(with S. Bagchi, R. Basak & R. Garg)

Journal of Fourier Analysis and Applications 29, 27 (2023).

Paper

1. Pointwise and Weighted Hessian Estimates for Kolmogorov-Fokker-Planck-type operators.

(with V. Tewary)

Annali di Matematica Pura ed Applicata(1923-), 2023.

Paper

1. Weighted inequalities for Fractional maximal functions on the infinite rooted k-ary tree.

(with E. Rela)

J Geom Anal 33, 34 (2023).

Paper

1. Weighted estimates for bilinear fractional integral operator on the Heisenberg group.

(with R. K. Singh)

Bulletin des Sciences Mathématiques, 103310 (2023).

Paper

Publications and Preprints:

1. Weighted estimates for lacunary maximal functions on homogeneous groups, preprint, arXiv:2411.01557.

(With Rajesh K. Singh)

Anal. Math. Phys. 16 (2026), no. 2, Paper No. 23, 22 pp.

Paper

1. Sparse bounds for oscillating multipliers on stratified groups.

(with M. Ruzhansky)

Monatsh. Math. 205 (2024), no. 3, 511–529.

Paper

1. On some operator-valued Fourier pseudo-multipliers associated to Grushin operators.

(with S. Bagchi, R. Basak & R. Garg)

Paper

Journal of Mathematical Analysis and Applications, Volume 539, Issue 1, Part 1, 2024.

1. Sharp weighted estimates for multi-linear Calderón-Zygmund operators on non-homogeneous spaces

(with A. Bhojak, P. Mohanty & S. Shrivastava)

Journal of Pseudo-Differential Operators and Applications, 11 (4), 2020, 1833–1867.

Paper

1. Lp regularity of Szegő projections on quotient domains.

(with G. Ghosh)

New York Journal of Mathematics, 29 (2023), 911-930.

Paper

1. Weighted inequalities for higher dimensional one-sided Hardy-Littlewood maximal function in Orlicz spaces.

(with P. Mohanty)

Expositiones Mathematicae, 40 (1), 2021, 23-44.

Paper

1. Weighted boundedness of multilinear maximal function using Dirac deltas.

(with S. Shrivastava & K. Shuin)

Rendiconti del Circolo Matematico di Palermo Series 2, 69 (1), 2020, 273–285.

Paper

1. Local One-Sided Maximal Function on Fractional Sobolev Spaces.

(with K. Shuin)

Mathematical Inequalities and Applications, 22 (2), 2019, 519–530.

Paper

1. Helical maximal function and weighted estimates, arXiv:2602.18359.

(with K. Shuin)

Paper

1. Bilinear spherical maximal function on the Heisenberg group, arXiv:2603.04068.

(with Rajesh K. Singh)

Paper

1. Bilinear Korányi spherical maximal function on the Heisenberg group,

(with Rajesh K. Singh)

Submitted to journal.

Book Chapters

One-sided Hardy-Littlewood maximal function on generalized Lorentz spaces.

(with P. Mohanty)

Extended Abstracts 2021/2022, Research Perspectives Ghent Analysis and PDE Center 2, Chapter 4. Link