14 citations · 61 across the 17 of their papers we have counts for
18 papers
On Besov and Triebel-Lizorkin spaces associated with the Grushin operator
Sayan Bagchi, Nishta Garg, Rahul Garg
In this article, we define classical and non-classical Besov and Triebel--Lizorkin spaces associated with the Grushin operator with or without drift. We establish various character…
On Sobolev spaces for the Grushin operator
Nishta Garg, Rahul Garg
We define Sobolev spaces associated with the Grushin operator with or without drift. We study some of their norm equivalences and establish embedding and algebra properties. We als…
Riesz transforms associated with the Grushin operator with drift
Nishta Garg, Rahul Garg
We consider the Grushin operator with drift which is symmetric with respect to a measure having exponential growth. For the corresponding Riesz transforms, we study strong-type $(p…
Quantum Hermite functions and Fourier Transform of operators
Rahul Garg, Sundaram Thangavelu
We construct operator analogues of Hermite functions which form an orthonormal basis for the Hilbert space of Hilbert-Schmidt operators on We use thi…
On some operator-valued Fourier pseudo-multipliers associated to Grushin operators
Sayan Bagchi, Riju Basak, Rahul Garg +1
This is a continuation of our work [BBGG23, BBGG22] where we have initiated the study of sparse domination and quantitative weighted estimates for Grushin pseudo-multipliers. In th…
Boundedness of certain linear operators on twisted Fock spaces
Rahul Garg, Sundaram Thangavelu
On the twisted Fock spaces we consider two types of convolution operators and associated to an element $ φ\in \mathcal{…
On extension of Calderón-Zygmund type singular integrals and their commutators
Sayan Bagchi, Rahul Garg, Joydwip Singh
Motivated by the recent works [Huan Yu, Quansen Jiu, and Dongsheng Li, 2021] and [Yanping Chen and Zihua Guo, 2021], we study the following extension of Calderón-Zygmund type singu…
Sparse bounds for pseudo-multipliers associated to Grushin operators, I
Sayan Bagchi, Riju Basak, Rahul Garg +1
In this article, we prove sharp quantitative weighted -estimates for Grushin pseudo-multipliers satisfying Hörmander's condition as an application of pointwise domination of G…
On -boundedness of pseudo-multipliers associated to the Grushin operator
Sayan Bagchi, Rahul Garg
In this article we define analogues of pseudo-differential operators associated to the joint functional calculus of the Grushin operator using their spectral resolution, and study…
Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group
Riju Basak, Rahul Garg, Sundaram Thangavelu
Inspired by the work of A. Bonami and S. Poornima that a non-constant function which is homogeneous of degree cannot be a Fourier multiplier on homogeneous Sobolev spaces, we e…
Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function
R. Garg, L. Roncal, S. Shrivastava
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in with finite overlapping. Quantitative weighted…
Localisation of Spectral Sums corresponding to the sub-Laplacian on the Heisenberg Group
Rahul Garg, K. Jotsaroop
In this article we study localisation of spectral sums associated to the sub-Laplacian on the Heisenberg Group where $S_R f := \int_0…
The lattice point counting problem on the Heisenberg groups
Rahul Garg, Amos Nevo, Krystal Taylor
We consider the radial and Heisenberg-homogeneous norms on the Heisenberg groups given by , for and . This nat…
On the role of Riesz potentials in Poisson's equation and Sobolev embeddings
Rahul Garg, Daniel Spector
In this paper, we study the mapping properties of the classical Riesz potentials acting on -spaces. In the supercritical exponent, we obtain new "almost" Lipschitz continuity…
On regularity of solutions to Poisson's equation
Rahul Garg, Daniel Spector
In this note, we announce new regularity results for some locally integrable distributional solutions to Poisson's equation. This includes, for example, the standard solutions obta…
Variations on a theorem of Beurling
Rahul Garg, Sundaram Thangavelu
We consider functions satisfying the subcritical Beurling's condition, viz., for some $ 0 < a…
On the structure of analytic vectors for the schrodinger representation
Rahul Garg, Sundaram Thangavelu
This article deals with the structure of analytic and entire vectors for the Schrödinger representations of the Heisenberg group. Using refined versions of Hardy's theorem and thei…
On the Hermite expansions of functions from Hardy class
Rahul Garg, Sundaram Thangavelu
Considering functions on for which both and are bounded by the Gaussian we show that their Fourier-Hermite coeffici…