14 citations · 61 across the 17 of their papers we have counts for
7 papers · 1 filter
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…
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…
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{…
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…
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 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…