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Weak type (1,1) multipliers on LCA groups

José Raposo (1997)

Studia Mathematica

In [ABB] Asmar, Berkson and Bourgain prove that for a sequence ϕ j j = 1 of weak type (1, 1) multipliers in n and a function k L 1 ( 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...

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