Pointwise Convergence to Initial Data of Heat and Hermite-Heat Equations in Modulation Spaces

Puntos clave

• This research aims to characterize weighted modulation spaces where the heat semigroup converges pointwise to initial data as time approaches zero.
• Characterization of weighted modulation spaces for heat semigroup convergence.
• Application of the standard Laplacian and Hermite operator in Euclidean space.
• Investigation of the Hardy-Littlewood maximal operator's properties on specific modulation spaces.
• Establishment of pointwise convergence for the heat semigroup on weighted modulation spaces.
• Demonstration that the Hardy-Littlewood maximal operator is applicable to certain modulation spaces.
• Identification of open questions regarding the relationship between modulation and Lebesgue spaces.

Resumen