Localisation of Bochner Riesz means corresponding to the sub-Laplacian on the Heisenberg Group

In this article we prove localisation of Bochner Riesz means $S_R$ of order $0$ for the sub-Laplacian $\mathcal{L}$ on the Heisenberg Group $\mathbb{H}^d.$ More precisely, we show that for any $0\eta$, $\lim_{R\rightarrow\infty}R^{-\beta/2} S_R f$ goes to $0$ a.e. on the set $\|(z,t)\|\leq 1$ for $f\in L^{2}(\mathbb{H}^d \setminus \{\|(z,t)\| \leq 3\}, \|(z,t)\|^{-\eta} \, dz \, dt).$ We generalise the method of Carbery and Soria (1988) in the context of $\mathbb{H}^d.$Comment: 20 page

on hardy and bmo spaces for grushin operator

We study Hardy and BMO spaces associated with the Grushin operator. We first prove atomic and maximal functions characterizations of the Hardy space. Further we establish a version of Fefferman–Stein decomposition of BMO functions associated with the Grushin operator and then obtain a Riesz transforms characterization of the Hardy space

Bilinear Bochner-Riesz square function and applications

In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and develop a systematic study of its $L^p$ boundedness properties. We also discuss applications of bilinear Bochner-Riesz square function in the context of bilinear fractional Schr\"{o}dinger multipliers, generalized bilinear spherical maximal function and more general bilinear multipliers defined on $\mathbb{R}^{2n}$ of the form $(\xi,\eta)\rightarrow m\left(|(\xi,\eta)|^2\right)$.Comment: Comments are welcom

Toeplitz operators with special symbols on Segal-Bargmann spaces

We study the boundedness of Toeplitz operators on Segal-Bargmann spaces in various contexts. Using Gutzmer's formula as the main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups. The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal-Bargmann spaces associated to Riemannian symmetric spaces of compact type

Toeplitz Operators with Special Symbols on Segal-Bargmann Spaces

We study the boundedness of Toeplitz operators on Segal-Bargmann spaces in various contexts. Using Gutzmer's formula as the main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups. The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal-Bargmann spaces associated to Riemannian symmetric spaces of compact type