Transference and restriction of maximal multiplier operators on Hardy spaces

Liu, Zhixin; Lu, Shanzhen

Studia Mathematica, Tome 104 (1993), p. 121-134 / Harvested from The Polish Digital Mathematics Library

Résumé

The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces $H^{p} (ℝ^{n})$ and $H^{p} (^{n})$ , 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an $L^{\infty} (ℝ^{n})$ function m is a maximal multiplier on $H^{p} (ℝ^{n})$ if and only if it is a maximal multiplier on $H^{p} (^{n})$ . As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered.

Publié le : 1993-01-01

Zbl 0812.42010

EUDML-ID : urn:eudml:doc:215988

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     author = {Zhixin Liu and Shanzhen Lu},
     title = {Transference and restriction of maximal multiplier operators on Hardy spaces},
     journal = {Studia Mathematica},
     volume = {104},
     year = {1993},
     pages = {121-134},
     zbl = {0812.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv105i2p121bwm}
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Liu, Zhixin; Lu, Shanzhen. Transference and restriction of maximal multiplier operators on Hardy spaces. Studia Mathematica, Tome 104 (1993) pp. 121-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv105i2p121bwm/

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