10 papers
Mixed Grushin Heat Equations with Riesz-Potential Nonlinearities in Marcinkiewicz Spaces: Subcritical, Critical, and Supercritical Regimes
Aparajita Dasgupta, Uttam Kumar Dolai
We study the nonlinear evolution equation where is the nonnegative self adjoint realization of Grushin o…
Uncertainty Principles for the Short-Time Fourier Transform on the Heisenberg Group
Arvish Dabra, Aparajita Dasgupta, Prerna Gulia
We develop a systematic theory of uncertainty principles for the short-time Fourier transform (STFT) on the Heisenberg group. Building on recent developments in modulation spaces a…
Hartee-type heat equation associated to fractional anharmonic oscillator on weighted modulation spaces
Aparajita Dasgupta, Uttam Kumar Dolai
We study Hartree-type nonlinear heat equations associated with fractional generalised anharmonic oscillators \(A_{k,l}\) in weighted modulation spaces. We first derive Strichartz-t…
Boundedness of Fourier Multipliers and Applications to Nonlinear PDEs for the Strichartz Fourier Transform on the Heisenberg Group
Aparajita Dasgupta, Prerna Gulia
We investigate Fourier multipliers associated with the Strichartz Fourier transform on the Heisenberg group. In particular, we establish Hörmander-type boundedness re…
Weighted Norm Inequalities for the Strichartz Fourier transform on the Heisenberg Group
Aparajita Dasgupta, Prerna Gulia, Sanjoy Pusti +1
In this article, we establish an analogue of Pitt's inequality for the Strichartz Fourier transform on the Heisenberg group . By exploiting the scalar-valued formulat…
Phase-Space Analysis of generalised Fractional Anharmonic and Ornstein-Uhlenbeck Semigroups on Weighted Modulation Spaces
Aparajita Dasgupta, Uttam Kumar Dolai
We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \…
Uncertainty Principles for the Strichartz Fourier transform on the Heisenberg Group
Arvish Dabra, Aparajita Dasgupta, Prerna Gulia
In this article, we establish several fundamental uncertainty principles for the Strichartz Fourier transform on the Heisenberg group, including Benedicks' theorem, the Donoho-Star…
-Heisenberg--Pauli--Weyl Uncertainty Inequalities on the Laguerre Hypergroup
Arvish Dabra, Aparajita Dasgupta
In this paper, we establish the first -Heisenberg--Pauli--Weyl uncertainty inequalities on the Laguerre hypergroup for the full range . These results extend Xiao's…
Some Versions of Beurling's Theorem on H-type Groups
Aparajita Dasgupta, Prerna Gulia, Sanjoy Pusti +1
We prove an analogue of Beurling's theorem on the H-type groups of certain dimensions after establishing the Gutzmer's formula for the H-type groups. We also obtain some other vers…
Localization operators on discrete Orlicz modulation spaces
Aparajita Dasgupta, Anirudha Poria
In this paper, we introduce Orlicz spaces on and Orlicz modulation spaces on , and study inclusion relations, convolution relations,…