Prasun Roychowdhury

activity

20202026

most citedHardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs

14 citations · 40 across the 21 of their papers we have counts for

collaborators

21 papers

math.AP2026

On the stability of eigenvalues of varying bilinear forms in abstract Hilbertian settings and applications

Andrea Bisterzo, Roberto Ognibene, Prasun Roychowdhury +1

The aim of the present paper is to develop a spectral perturbation theory from a higher perspective. More precisely, we consider a one-parameter family of varying bilinear forms, e…

math.AP2026

Profile decomposition and multiple positive solutions for the perturbed CR Yamabe equation on the Heisenberg group

Riju Basak, Souptik Chakraborty, Tapendu Rana +1

In this article, we study an inhomogeneous critical nonlinear equation involving the sub-Laplacian on the Heisenberg group $H^{n}$ . We prove the multiplicity of positive solu…

math.AP2026

Sharp Quantitative Forms of the Hardy Inequality on Cartan-Hadamard Manifolds via Sobolev-Lorentz Embeddings

Avas Banerjee, Debdip Ganguly, Prasun Roychowdhury

In this article, we investigate the quantitative form of the classical Hardy inequality. In our first result, we prove the following quantitative bound under the assumption that th…

math.FA2025

Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content

Riju Basak, You-Wei Benson Chen, Prasun Roychowdhury

We study the action of uncentered fractional maximal functions on mean oscillation spaces associated with the dyadic Hausdorff content $H_{\infty}^{β}$ with $0 < β \leq n$ . Fo…

math.AP2025

Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields

Avas Banerjee, Riju Basak, Prasun Roychowdhury

In this paper, we improve the $L^{p}$ -Rellich and Hardy-Rellich inequalities in the setting of radial Baouendi-Grushin vector fields. We establish an identity relating the subcritica…

math.FA2025

The Capacitary John-Nirenberg Inequality Revisited

Riju Basak, You-Wei Benson Chen, Prasun Roychowdhury +1

In this paper, we establish maximal function estimates, Lebesgue differentiation theory, Calderón-Zygmund decompositions, and John-Nirenberg inequalities for translation invariant…

math.AP2024

On sharp constants in higher order Adams-Cianchi inequalities

Prasun Roychowdhury, Daniel Spector

The main results of this paper are the establishment of sharp constants for several families of critical Sobolev embeddings. These inequalities were pioneered by David R. Adams, wh…

math.AP2024

Hardy and Rellich identities and inequalities for Baouendi-Grushin operators via spherical vector fields

Debdip Ganguly, K. Jotsaroop, Prasun Roychowdhury

For Baouendi-Grushin vector fields, we prove Hardy, Hardy-Rellich, and Rellich identities and inequalities with sharp constants. Our explicit remainder terms significantly improve…

math.AP2024

Critical, stability and higher-order analysis for Hardy type inequalities on Cartan-Hadamard manifolds

Prasun Roychowdhury, Durvudkhan Suragan, Nurgissa Yessirkegenov

In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain…

math.FA2023

One-dimensional integral Rellich type inequalities

Tohru Ozawa, Prasun Roychowdhury, Durvudkhan Suragan

The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality ver…

math.AP2022★ 3 cited

Classification of radial solutions to $- Δ_{g} u = e^{u}$ on Riemannian models

Elvise Berchio, Alberto Ferrero, Debdip Ganguly +1

We provide a complete classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation $- Δ_{g} u = e^{u}$ on Riemann…

math.FA2022★ 2 cited

Multidimensional Frank-Laptev-Weidl improvement of the Hardy Inequality

Prasun Roychowdhury, Michael Ruzhansky, Durvudkhan Suragan

We establish a new improvement of the classical $L^{p}$ -Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new ki…

math.FA2022★ 4 cited

Improvement of the discrete Hardy inequality

Prasun Roychowdhury, Durvudkhan Suragan

We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our a…

math.AP2022★ 1 cited

Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space

Debdip Ganguly, Prasun Roychowdhury

We prove an improved version of Poincaré-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Har…

math.AP2022

Stochastic completeness and $L^{1}$ -Liouville property for second-order elliptic operators

Debdip Ganguly, Yehuda Pinchover, Prasun Roychowdhury

Let $P$ be a linear, second-order, elliptic operator with real coefficients defined on a noncompact Riemannian manifold $M$ and satisfies $P 1 = 0$ in $M$ . Assume further that $P$ adm…

math.AP2021★ 14 cited

Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs

Elvise Berchio, Debdip Ganguly, Prasun Roychowdhury

We prove a family of Hardy-Rellich and Poincaré identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Po…

math.AP2021★ 3 cited

On ergodic control problem for viscous Hamilton--Jacobi equations for weakly coupled elliptic systems

Ari Arapostathis, Anup Biswas, Prasun Roychowdhury

In this article we study ergodic problems in the whole space $R^{N}$ for weakly coupled systems of viscous Hamilton-Jacobi equations with coercive right-hand sides. The Hami…

math.AP2020★ 2 cited

Generalized principal eigenvalues on $R^{d}$ of second order elliptic operators with rough nonlocal kernels

Ari Arapostathis, Anup Biswas, Prasun Roychowdhury

We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has…

math.FA2020★ 2 cited

On Higher order Poincaré Inequalities with radial derivatives and Hardy improvements on the hyperbolic space

Prasun Roychowdhury

In this paper we prove higher order Poincaré inequalities involving radial derivatives namely, \begin{equation*} \int_{\mathbb{H}^{N}} |\nabla_{r,\mathbb{H}^{N}}^{k} u|^2 \, {\rm d…

math.AP2020★ 3 cited

Generalized principal eigenvalues of convex nonlinear elliptic operators in $R^{N}$

Anup Biswas, Prasun Roychowdhury

We study the generalized eigenvalue problem in $R^{N}$ for a general convex nonlinear elliptic operator which is locally elliptic and positively $1$ -homogeneous. Generalizin…

math.FA2020★ 6 cited

On some strong Poincaré inequalities on Riemannian models and their improvements

Elvise Berchio, Debdip Ganguly, Prasun Roychowdhury

We prove second and fourth order improved Poincaré type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part…

On the stability of eigenvalues of varying bilinear forms in abstract Hilbertian settings and applications

Profile decomposition and multiple positive solutions for the perturbed CR Yamabe equation on the Heisenberg group

Sharp Quantitative Forms of the Hardy Inequality on Cartan-Hadamard Manifolds via Sobolev-Lorentz Embeddings

Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content

Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields

The Capacitary John-Nirenberg Inequality Revisited

On sharp constants in higher order Adams-Cianchi inequalities

Hardy and Rellich identities and inequalities for Baouendi-Grushin operators via spherical vector fields

Critical, stability and higher-order analysis for Hardy type inequalities on Cartan-Hadamard manifolds

One-dimensional integral Rellich type inequalities

Classification of radial solutions to −Δg​u=eu on Riemannian models

Multidimensional Frank-Laptev-Weidl improvement of the Hardy Inequality

Improvement of the discrete Hardy inequality

Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space

Stochastic completeness and L1-Liouville property for second-order elliptic operators

Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs

On ergodic control problem for viscous Hamilton--Jacobi equations for weakly coupled elliptic systems

Generalized principal eigenvalues on Rd of second order elliptic operators with rough nonlocal kernels

On Higher order Poincaré Inequalities with radial derivatives and Hardy improvements on the hyperbolic space

Generalized principal eigenvalues of convex nonlinear elliptic operators in RN

On some strong Poincaré inequalities on Riemannian models and their improvements

Classification of radial solutions to $- Δ_{g} u = e^{u}$ on Riemannian models

Stochastic completeness and $L^{1}$ -Liouville property for second-order elliptic operators

Generalized principal eigenvalues on $R^{d}$ of second order elliptic operators with rough nonlocal kernels

Generalized principal eigenvalues of convex nonlinear elliptic operators in $R^{N}$