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On operators with complex Gaussian kernels over Lp spaces

González B.J. (Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de La Laguna (ULL), Campus de Anchieta, ES-La Laguna (Tenerife), España)
Negrína E.R. (Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de La Laguna (ULL), Campus de Anchieta, ES-La Laguna (Tenerife), España)

In this paper we study new Lp-boundedness properties and Parseval-type relations concerning the operators with complex Gaussian kernels over the spaces Lp(R,w(x)dx), 1 ≤ p ≤ ∞, where w represents any function greater than or equal to one almost everywhere on R. Here, the Gauss-Weierstrass semigroup is considered as a particular case of this analysis.

Keywords: Complex Gaussian kernels, Lp-Inequalities, Parseval-type relations, Gauss-Weierstrass semigroup