arXiv subjects

P. K. Sanjay

Publications and source records attributed to P. K. Sanjay.

4 recordsLinked to original sources

arXiv2021

Injectivity of spherical means on H-type groups

We establish injectivity results for three different spherical means on an $H$-type group, $G$. First is the standard spherical means which is defined to be the average of a function over the spheres in the complement of the center, second is the average over the product of spheres in the center and its complement, and the third is the average over the spheres defined by a homogeneous norm on $G$. If $m$ is the dimension of the center of $G$, injectivity of these spherical means is proved for the range $1 \leq p \leq \frac{2m}{m-1}$. Examples are provided to show the sharpness of our results in the first two cases.

math.FA↗

arXiv2012

Dimension free boundedness of Riesz transforms for the Grushin operator

Let $G = - Δ_ξ - |ξ|^2 \frac{\partial^2}{\partial η^2}$ be the Grushin operator on $\R^n \times \R.$ We prove that the Riesz transforms associated to this operator are bounded on $L^p (\R^{n+1}), 1 < p < \infty$ and their norms are independent of the dimension $n$.

math.FA↗

arXiv2011

Riesz transforms and multipliers for the Grushin operator

We show that Riesz transforms associated to the Grushin operator G = -Δ- |x|^2\partial_t^2 are bounded on L^p(R^n+1). We also establish an analogue of Hörmander-Mihlin multiplier theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator valued Fourier multiplier theorem due to L. Weis.

math.FA↗

arXiv2011

Revisiting Riesz transforms on Heisenberg groups

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transfer- ence theorems, we deduce boundedness theorems for Riesz trans- forms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre ex- pansions.

math.FA↗