A Continuous Characterization of Triebel-Lizorkin Spaces Associated with Hermite Expansions

الملخص EN

We study the properties of the Triebel-Lizorkin spaces associated with the multidimensional Hermite expansions on Rd (d≥1).

In addition to the endpoint estimates, we give the continuous characterizations of these spaces via harmonic and thermic extensions from Rd into R+d+1.

Based on this result, we obtain the boundedness of Riesz transform associated with the Hermite expansions.