Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Weisz, Ferenc

Weisz, Ferenc

Studia Mathematica, Tome 119 (1996), p. 173-194 / Harvested from The Polish Digital Mathematics Library

Résumé

The martingale Hardy space $H_{p} ({[0, 1)}^{2})$ and the classical Hardy space $H_{p} (^{2})$ are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from $H_{p}$ to $L_{p}$ (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a Marcinkiewicz-Zygmund type inequality is obtained for BMO spaces.

Publié le : 1996-01-01

Zbl 0839.42009

EUDML-ID : urn:eudml:doc:216250

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     author = {Ferenc Weisz},
     title = {Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {173-194},
     zbl = {0839.42009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv117i2p173bwm}
}

Weisz, Ferenc. Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series. Studia Mathematica, Tome 119 (1996) pp. 173-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv117i2p173bwm/

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