A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

Wojciechowski, Michał

Studia Mathematica, Tome 141 (2000), p. 273-287 / Harvested from The Polish Digital Mathematics Library

Résumé

It is proved that if $m : ℝ^{d} \to ℂ$ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the $H^{1}$ space on the product domain $ℝ^{d_{1}} \times . . . \times ℝ^{d_{k}}$ . This implies an estimate of the norm $N (m, L^{p} (ℝ^{d})$ of the multiplier transformation of m on $L^{p} (ℝ^{d})$ as p→1. Precisely we get $N (m, L^{p} (ℝ^{d})) ≲ {(p - 1)}^{- k}$ . This bound is the best possible in general.

Publié le : 2000-01-01

Zbl 0982.42004

EUDML-ID : urn:eudml:doc:216767

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     author = {Micha\l\ Wojciechowski},
     title = {A Marcinkiewicz type multiplier theorem for H$^1$ spaces on product domains},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {273-287},
     zbl = {0982.42004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv140i3p273bwm}
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Wojciechowski, Michał. A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains. Studia Mathematica, Tome 141 (2000) pp. 273-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv140i3p273bwm/

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