Pointwise and grand maximal function characterizations of Besov-type and Triebel-Lizorkin-type spaces

الأصل · EN

In this note, we establish characterizations for the homogeneous Besov-type spaces Bˢ,τₚ,q(Rⁿ) and Triebel-Lizorkin-type spaces Fˢ,τₚ,q(Rⁿ), introduced by Yang and Yuan, through fractional Hajłasz-type gradients for suitable values of the parameters p, q and τ when 0 < s < 1, and through grand Littlewood-Paley-type maximal functions for all admissible values of the parameters. These characterizations extend the characterizations obtained by Koskela, Yang and Zhou for the standard homogeneous Besov and Triebel-Lizorkin spaces.