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In this paper, we obtain a characterization of $$H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})$$ H Δ ν p ( R + n ) Hardy spaces by using atoms associated with the radial maximal function, the nontangential maximal function and the grand maximal function related to $$\varDelta _{\nu }$$ Δ ν Laplace–Bessel operator for $$\nu >0$$ ν > 0 and $$1<p<\infty $$ 1 < p < ∞ . As an application, we further establish an atomic characterization of Hardy spaces $$H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})$$ H Δ ν p ( R + n ) in terms of the high order Riesz–Bessel transform for $$0<p\le 1$$ 0 < p ≤ 1 .
Analysis and Mathematical Physics – Springer Journals
Published: Jul 22, 2019
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