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Complex Analysis and Operator Theory

, Volume 11, Issue 3, pp 603–610 | Cite as

Parseval-Type Relations and \(L^p\)-Inequalities for the Operators with Complex Gaussian Kernels

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Abstract

In this paper we study new \(L^p\)–boundedness properties for the integral transform with complex Gaussian kernel over \(L^p ({\mathbb {R}},(1+x^2)^{\alpha } dx)\), \(1\le p \le \infty \), \(\alpha \in {\mathbb {R}}\). We also obtain Parseval-type relations over these spaces. The Gauss–Weierstrass semigroup on \({\mathbb {R}}\) is analyzed as a particular case.

Keywords

Complex Gaussian kernels \(L^p\)-Inequalities Parseval-type relations Gauss–Wierstrass semigroup 

Mathematics Subject Classification

Primary 44A15 Secondary 46E30 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático Facultad de CienciasUniversidad de La Laguna (ULL) Campus de AnchietaLa Laguna (Tenerife)Spain

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