Lusin Characterisation of Hardy Spaces Associated with Hermite Operators
https://doi.org/10.1007/s10476-020-0016-zPublisher, magazine: ,
Publication year: 2020
Lưu Trích dẫn Chia sẻAbstract
Let d ∈ {3, 4, 5,...} and p ∈ (0, 1]. We consider the Hermite operator L = −Δ + |x|2 on its maximal domain in L2(ℝd). Let HpL(Rd) be the completion of {f∈L2(Rd):MLf∈Lp(Rd)} with respect to the quasi-norm ∥⋅∥HpL=∥ML⋅∥Lp, where MLf(⋅)=supt>0∣∣e−tLf(⋅)∣∣ for all f ∈ L2(ℝd). We characterise HpL(Rd) in terms of Lusin integrals associated with the Hermite operator for p∈(dd+1,1].
Tags: Hermite operator; Hardy space; Lusin integral; atom decomposition; heat kernel; Poisson semigroup