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Cesàro summability of one- and two-dimensional trigonometric-Fourier series

Ferenc Weisz (1997)

Colloquium Mathematicae

We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from L to L then it is also bounded from the classical Hardy space H p ( T ) to L p (0 < p ≤ 1). As an application it is shown that the maximal operator of the one-parameter Cesàro means of a distribution is bounded from H p ( T ) to L p (3/4 < p ≤ ∞) and is of weak type ( L 1 , L 1 ) . We define the two-dimensional dyadic hybrid Hardy space H 1 ( T 2 ) and verify that the maximal operator of the Cesàro means of a two-dimensional...

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