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

Weisz, Ferenc

Weisz, Ferenc

Colloquium Mathematicae, Tome 72 (1997), p. 123-133 / Harvested from The Polish Digital Mathematics Library

Résumé

We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from $L_{\infty}$ to $L_{\infty}$ 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 function is of weak type $(H_{1}^{♯} (T^{2}), L_{1})$ . So we deduce that the two-parameter Cesàro means of a function $f \in H_{1}^{♯} (T^{2}) \supset L l o g L$ converge a.e. to the function in question.

Publié le : 1997-01-01

Zbl 0891.42006

EUDML-ID : urn:eudml:doc:210495

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     author = {Ferenc Weisz},
     title = {Ces\`aro summability of one- and two-dimensional trigonometric-Fourier series},
     journal = {Colloquium Mathematicae},
     volume = {72},
     year = {1997},
     pages = {123-133},
     zbl = {0891.42006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv74i1p123bwm}
}

Weisz, Ferenc. Cesàro summability of one- and two-dimensional trigonometric-Fourier series. Colloquium Mathematicae, Tome 72 (1997) pp. 123-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv74i1p123bwm/

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