Extensions of Fatou theorems in products of upper half-spaces. (English) Zbl 0841.42008

Svensson, Olof

Math. Scand. 76, No. 1, 139-151 (1995).

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).

Reviewer: O.Svensson (Göteborg)

MSC:

42B25

Maximal functions, Littlewood-Paley theory

Keywords:

Fatou theorems; maximal function; Carleson measure; weak type (1,1)