On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Tateoka, Jun

Tateoka, Jun

Studia Mathematica, Tome 108 (1994), p. 127-148 / Harvested from The Polish Digital Mathematics Library

Résumé

C. Watari [12] obtained a simple characterization of Lipschitz classes $L i p^{(p)} α (W) (1 \geq p \geq \infty, α > 0)$ on the dyadic group using the $L^{p}$ -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B_{p, q}^{α}$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B_{p, q}^{α}$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality of the type of the Maz’ya inequality, a weak type estimate for maximal Cesàro means and a sufficient condition of absolute convergence of Walsh-Fourier series.

Publié le : 1994-01-01

Zbl 0817.43004

EUDML-ID : urn:eudml:doc:216105

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     author = {Jun Tateoka},
     title = {On the characterization of Hardy-Besov spaces on the dyadic group and its applications},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {127-148},
     zbl = {0817.43004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv110i2p127bwm}
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Tateoka, Jun. On the characterization of Hardy-Besov spaces on the dyadic group and its applications. Studia Mathematica, Tome 108 (1994) pp. 127-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv110i2p127bwm/

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