A remark on extrapolation of rearrangement operators on dyadic $H^{s}$, 0 < s ≤ 1

Stefan Geiss; Paul F. X. Müller; Veronika Pillwein

A remark on extrapolation of rearrangement operators on dyadic

H^{s}

, 0 < s ≤ 1

Stefan Geiss ; Paul F. X. Müller ; Veronika Pillwein

Studia Mathematica, Tome 166 (2005), p. 196-205 / Harvested from The Polish Digital Mathematics Library

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Résumé

For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator $T_{s}$ , 0 < s < 2, to be the linear extension of the map $(h_{I}) / {(| I |}^{1 / s}) \mapsto (h_{τ (I)}) (| τ (I) |^{1 / s})$ , where $h_{I}$ denotes the $L^{\infty}$ -normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that $T_{s ₀}$ is bounded on $H^{s ₀}$ , then for all 0 < s < 2 the operator $T_{s}$ is bounded on $H^{s}$ .

Publié le : 2005-01-01

Zbl 1092.46014

EUDML-ID : urn:eudml:doc:286642

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     title = {A remark on extrapolation of rearrangement operators on dyadic $H^{s}$, 0 < s $\leq$ 1},
     journal = {Studia Mathematica},
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     year = {2005},
     pages = {196-205},
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Stefan Geiss; Paul F. X. Müller; Veronika Pillwein. A remark on extrapolation of rearrangement operators on dyadic $H^{s}$, 0 < s ≤ 1. Studia Mathematica, Tome 166 (2005) pp. 196-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm171-2-5/