A Continuous Characterization of Triebel-Lizorkin Spaces Associated with Hermite Expansions. (28th May 2015) - Gong, Shuli; Ma, Bolin; Fu, Zunwei
Abstract : We study the properties of the Triebel-Lizorkin spaces associated with the multidimensional Hermite expansions onR d (d ≥ 1 ). In addition to the endpoint estimates, we give the continuous characterizations of these spaces via harmonic and thermic extensions fromR d intoR + d + 1 . Based on this result, we obtain the boundedness of Riesz transform associated with the Hermite expansions.