Geodesic
Weak type (1,1) multipliers on LCA groups
Studia Mathematica, Tome 122 (1997) no. 2, pp. 123-130

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In [ABB] Asmar, Berkson and Bourgain prove that for a sequence ${ϕ_j}^∞_{j=1} $ of weak type (1, 1) multipliers in $ℝ^n$ and a function $k ∈ L^1(ℝ^n)$ 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.
DOI : 10.4064/sm-122-2-123-130
Keywords: weak type multipliers, maximal operators, vector inequalities

José A Raposo 1

1 
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José A  Raposo. Weak type (1,1) multipliers on LCA groups. Studia Mathematica, Tome 122 (1997) no. 2, pp. 123-130. doi: 10.4064/sm-122-2-123-130

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