Hi, I'm Abhishek, a postdoctoral fellow at Institute of Mathematics, Polish Academy of Sciences (Link ). 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@gmail.com; agosh@impan.pl
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.
Publications
Decay at infinity for solutions to some fractional parabolic equations.
(with A. Banerjee)
To appear in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics.
Sparse bounds for pseudo-multipliers associated to Grushin operators, II.
(with S. Bagchi, R. Basak & R. Garg)
J Geom Anal 34, 34 (2024).
Strong unique continuation for variable coefficient parabolic operators with Hardy type potential.
(with A. Banerjee & P. Ganguly)
J. Differential Equations 380 (2024), 92-145.
Pointwise and Weighted Hessian Estimates for Kolmogorov-Fokker-Planck-type operators.
(with V. Tewary)
Annali di Matematica Pura ed Applicata(1923-), 2023.
Weighted estimates for bilinear fractional integral operator on the Heisenberg group.
(with R. K. Singh)
Bulletin des Sciences Mathématiques, 103310 (2023).
Lp regularity of Szegő projections on quotient domains.
(with G. Ghosh)
New York Journal of Mathematics, 29 (2023), 911-930.
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).
Weighted inequalities for Fractional maximal functions on the infinite rooted k-ary tree.
(with E. Rela)
J Geom Anal 33, 34 (2023).
Weighted inequalities for higher dimensional one-sided Hardy-Littlewood maximal function in Orlicz spaces.
(with P. Mohanty)
Expositiones Mathematicae, 40 (1), 2021, 23-44.
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.
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.
Local One-Sided Maximal Function on Fractional Sobolev Spaces.
(with K. Shuin)
Mathematical Inequalities and Applications, 22 (2), 2019, 519–530.
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
Preprints
Spherical maximal functions and Hardy spaces for Fourier integral operators.
(with N. Liu, J. Rozendaal, L. Song)
Sharp asymptotic of solutions to some nonlocal parabolic equations.
(with A. Banerjee)
On some operator-valued Fourier pseudo-multipliers associated to Grushin operators.
(with S. Bagchi, R. Basak & R. Garg)
Sparse bounds for oscillating multipliers on stratified groups.
(with M. Ruzhansky)