Geodesic
The local versions of $H^p(ℝ^n)$ spaces at the origin
Studia Mathematica, Tome 116 (1995) no. 2, pp. 103-131

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Let 0 p ≤ 1 q ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces $HK̇_q^{α,p}(ℝ^n)$ which are the local versions of $H^p(ℝ^n)$ spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizations in M. Frazier and B. Jawerth's sense. We also prove an interpolation theorem for operators on $HK̇_q^{α,p}(ℝ^n)$ and discuss the $HK̇_q^{α,p}(ℝ^n)$-boundedness of Calderón-Zygmund operators. Similar results can also be obtained for the non-homogeneous Hardy spaces $HK_q^{α,p}(ℝ^n)$.
DOI : 10.4064/sm-116-2-103-131

Shan Zhen Lu 1

1 
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Shan Zhen Lu. The local versions of $H^p(ℝ^n)$ spaces at the origin. Studia Mathematica, Tome 116 (1995) no. 2, pp. 103-131. doi: 10.4064/sm-116-2-103-131

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