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, preprint, arXiv:2401.16955.

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

To appear in J Geom Anal.

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

(with E. Rela)

J Geom Anal 33, 34 (2023).

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

(with A. Banerjee)

Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, pp. 1–37, 2024.

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 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)

To appear in Analysis and Mathematical Physics.

Paper

1. Sparse bounds for oscillating multipliers on stratified groups.

(with M. Ruzhansky)

Accepted for publication in Monatshefte für Mathematik.

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

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