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Extensions of Fatou theorems in products of upper half-spaces. (English) Zbl 0841.42008
We consider a multiparameter maximal operator and give a necessary and sufficient condition for its boundedness on $$L^p$$, $$p> 1$$. We also prove that the maximal operator with suitable restrictions on the parameters, is of weak type (1,1).

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory
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