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I work in the field of research related to harmonic analysis and PDE's on hyperbolic spaces, Lie groups and homogeneous trees. During my Ph.D., my research has primarily revolved around Wiener Tauberian theorems on semisimple Lie groups. Currently, I am engaged in problems related to Functional and Fourier inequalities and exploring their applications in Partial Differential Equations. Additionally, I am involved in research on the weighted estimates of integral operators.
I work in the field of research related to harmonic analysis and PDE's on hyperbolic spaces, Lie groups and homogeneous trees. During my Ph.D., my research has primarily revolved around Wiener Tauberian theorems on semisimple Lie groups. Currently, I am engaged in problems related to Functional and Fourier inequalities and exploring their applications in Partial Differential Equations. Additionally, I am involved in research on the weighted estimates of integral operators.
Book Edited
Methusalem Seminars at Ghent Analysis and PDE Center. Extended Abstracts 2023/2024. Editors: David Santiago Gomez Cobos, Tapendu Rana, Michael Ruzhansky. Research Perspectives Ghent Analysis and PDE Center, Trends in Mathematics, Birkhäuser, 2026. DOI.
Published / Accepted articles
L^p-L^q Fourier multipliers and Hausdorff-Young-Paley inequalities on Riemannian symmetric spaces of noncompact type. Tapendu Rana, Michael Ruzhansky. Journal of Geometric Analysis, 2026. DOI, arXiv.
Weighted estimates for Hardy-Littlewood maximal functions on Harmonic NA groups. Pritam Ganguly, Tapendu Rana, Jayanta Sarkar. Mathematische Zeitschrift 310, Paper No. 55, 2025. DOI, arXiv.
Pseudo-differential operators on radial sections of line bundles over the Poincaré upper half plane. Tapendu Rana, Michael Ruzhansky. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2024. DOI. arXiv.
L^p-boundedness of pseudo-differential operators on rank one Riemannian symmetric spaces of noncompact type. Tapendu Rana, Sanjoy Pusti. Mathematische Zeitschrift 305, Paper No. 2, 2023. DOI , arXiv.
L^p-boundedness of pseudo-differential operators on homogeneous trees.Tapendu Rana, Sumit Kumar Rano. Studia Mathematica 272(3), 221–244, 2023. DOI, arXiv.
Wiener Tauberian theorems for certain Banach algebras on real rank one semisimple Lie groups. Tapendu Rana. Journal of the Australian Mathematical Society, 2023. DOI.
A genuine analogue of the Wiener Tauberian theorem for some Lorentz spaces on SL(2,ℝ). Tapendu Rana. Forum Mathematicum 33, 213–243, 2021. DOI, arXiv .
Preprints
Fourier inequalities and general monotonicity in hyperbolic geometry. Dmitry V. Gorbachev, Tapendu Rana, Sergey Yu. Tikhonov. Preprint (2026).
Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces. Tapendu Rana, 2026. Submitted. arXiV.
Topological Effects on Bubbling in the Critical Dirichlet Problem on Hyperbolic Domains: 3≤N≤5. Tapendu Rana, Michael Ruzhansky, Zhipeng Yang, 2026. Submitted. arXiv.
Profile decomposition and multiple positive solutions for the perturbed CR Yamabe equation on the Heisenberg group with Riju Basak, Souptik Chakraborty, Tapendu Rana, Prasun Roychowdhury, 2026. Submitted. arXiv.
Multiplicity of solutions to the Brezis-Nirenberg problem on hyperbolic spaces with Sekhar Ghosh, Vishvesh Kumar, 2026. Submitted. arXiv.
Shifted Pitt and uncertainty inequalities on Riemannian symmetric spaces of noncompact type with Michael Ruzhansky, 2025. Submitted. arXiv.
Classical inequalities for all Fourier matrix coefficients of SL(2,ℝ) and their applications with Vishvesh Kumar, Michael Ruzhansky, 2024. Submitted. arXiv
Weighted Fourier inequalities and application of restriction theorems on rank one Riemannian symmetric spaces of noncompact type with Pratyoosh Kumar, Sanjoy Pusti, Mandeep Singh, 2024. Submitted. arXiv
Book Chapters
Recent Advances in Harmonic Analysis on the Group SL(2, R). In: Kumar, V., Rottensteiner, D., Ruzhansky, M. (eds) Pseudo-Differential Operators and Related Topics. PSORT 2024. Trends in Mathematics(), vol 8. Birkhäuser, Cham. DOI
A Note on Boundedness Properties of Pseudo-Differential Operators on Rank One Symmetric Spaces of Noncompact Type. In: Ruzhansky, M., Van Bockstal, K. (eds) Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics(), vol 2. Birkhäuser, Cham. DOI.
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