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Hardy spaces for the Dunkl harmonic oscillator
Author(s) -
Hejna Agnieszka
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900215
Subject(s) - mathematics , harmonic oscillator , hardy space , laplace operator , space (punctuation) , maximal function , semigroup , riesz transform , pure mathematics , harmonic function , harmonic , type (biology) , mathematical analysis , quantum mechanics , physics , linguistics , ecology , philosophy , biology
Let Δ and L = Δ − ∥ x ∥ 2be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space H 1 associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup e t L . We prove that the space H 1 admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic decompositions are of local type.