Multiplier transformations on $H^{p}$ spaces

Chen, Daning; Fan, Dashan

Multiplier transformations on

H^{p}

spaces

Chen, Daning ; Fan, Dashan

Studia Mathematica, Tome 129 (1998), p. 189-204 / Harvested from The Polish Digital Mathematics Library

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Résumé

The authors obtain some multiplier theorems on $H^{p}$ spaces analogous to the classical $L^{p}$ multiplier theorems of de Leeuw. The main result is that a multiplier operator ${(T f)}^{(} x) = λ (x) f ̂ (x)$ $(λ \in C (ℝ^{n}))$ is bounded on $H^{p} (ℝ^{n})$ if and only if the restriction ${λ (ε m)}_{m \in Λ}$ is an $H^{p} (T^{n})$ bounded multiplier uniformly for ε>0, where Λ is the integer lattice in $ℝ^{n}$ .

Publié le : 1998-01-01

Zbl 1050.42010

EUDML-ID : urn:eudml:doc:216575

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     author = {Daning Chen and Dashan Fan},
     title = {Multiplier transformations on $H^{p}$ spaces},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {189-204},
     zbl = {1050.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p189bwm}
}

Chen, Daning; Fan, Dashan. Multiplier transformations on $H^{p}$ spaces. Studia Mathematica, Tome 129 (1998) pp. 189-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p189bwm/

Bibliographie

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