New Lp-inequalities for hyperbolic weights concerning the operators with complex Gaussian kernels

Abstract

In this article the authors present a systematic study of several new $L^p$-boundedness properties and Parseval-type relations concerning the operators with complex Gaussian kernels over the spaces $L^p(\mathbb{R},cosh(\alpha x\left)dx\right)$ and $L^p(\mathbb{R},cosh(\alpha x^2\left)dx\right)$, $1\le p\le \infty$, $\alpha \in \mathbb{R}$. Relevant connections with various earlier related results are also pointed out.