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

Benito J. González; Emilio R. Negrín

doi:10.1215/17358787-2017-0025

April 2018 New

L^{p}

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

Benito J. González, Emilio R. Negrín

Banach J. Math. Anal. 12(2): 399-421 (April 2018). DOI: 10.1215/17358787-2017-0025

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 $L^{p}(\mathbb{R},\cosh(\alpha x)\,dx)$ and $L^{p}(\mathbb{R},\cosh(\alpha x^{2})\,dx)$ , $1\leq p\leq\infty$ , $\alpha\in\mathbb{R}$ . Relevant connections with various earlier related results are also pointed out.

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Benito J. González and Emilio R. Negrín "New

L^{p}

-inequalities for hyperbolic weights concerning the operators with complex Gaussian kernels," Banach Journal of Mathematical Analysis 12(2), 399-421, (April 2018). https://doi.org/10.1215/17358787-2017-0025

Received: 24 February 2017; Accepted: 20 June 2017; Published: April 2018

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Benito J. González, Emilio R. Negrín "New

L^{p}

-inequalities for hyperbolic weights concerning the operators with complex Gaussian kernels," Banach Journal of Mathematical Analysis, Banach J. Math. Anal. 12(2), 399-421, (April 2018)

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