The local versions of $H^p(ℝ^n)$ spaces at the origin

Lu, Shan; Yang, Da

The local versions of

H^{p} (ℝ^{n})

spaces at the origin

Lu, Shan ; Yang, Da

Studia Mathematica, Tome 113 (1995), p. 103-131 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces $H K ̇_{q}^{α, p} (ℝ^{n})$ 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 $H K ̇_{q}^{α, p} (ℝ^{n})$ and discuss the $H K ̇_{q}^{α, p} (ℝ^{n})$ -boundedness of Calderón-Zygmund operators. Similar results can also be obtained for the non-homogeneous Hardy spaces $H K_{q}^{α, p} (ℝ^{n})$ .

Publié le : 1995-01-01

Zbl 0935.42012

EUDML-ID : urn:eudml:doc:216223

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     author = {Shan Lu and Da Yang},
     title = {The local versions of $H^p($\mathbb{R}$^n)$ spaces at the origin},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {103-131},
     zbl = {0935.42012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i2p103bwm}
}

Lu, Shan; Yang, Da. The local versions of $H^p(ℝ^n)$ spaces at the origin. Studia Mathematica, Tome 113 (1995) pp. 103-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i2p103bwm/

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