Weak type (1,1) multipliers on LCA groups

Raposo, José

Raposo, José

Studia Mathematica, Tome 122 (1997), p. 123-130 / Harvested from The Polish Digital Mathematics Library

Résumé

In [ABB] Asmar, Berkson and Bourgain prove that for a sequence ${ϕ_{j}}_{j = 1}^{\infty}$ of weak type (1, 1) multipliers in $ℝ^{n}$ and a function $k \in L^{1} (ℝ^{n})$ the weak type (1,1) constant of the maximal operator associated with ${k ⁎ ϕ_{j}}_{j}$ is controlled by that of the maximal operator associated with ${ϕ_{j}}_{j}$ . In [ABG] this theorem is extended to LCA groups with an extra hypothesis: the multipliers must be continuous. In this paper we prove a more general version of this last result without assuming the continuity of the multipliers. The proof arises after simplifying the one in [ABB] which becomes then extensible to LCA groups.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216364

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     author = {Jos\'e Raposo},
     title = {Weak type (1,1) multipliers on LCA groups},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {123-130},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv122i2p123bwm}
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Raposo, José. Weak type (1,1) multipliers on LCA groups. Studia Mathematica, Tome 122 (1997) pp. 123-130. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv122i2p123bwm/

Bibliographie

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[00001] [ABG] N. Asmar, E. Berkson and T. A. Gillespie, Convolution estimates and generalized de Leuw Theorems for multipliers of weak type (1, 1), Canad. J. Math. 47 (1995), 225-245.

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