On the characterization of Hardy-Besov spaces on the dyadic group and its applications
Studia Mathematica, Tome 110 (1994) no. 2, pp. 127-148
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
C. Watari [12] obtained a simple characterization of Lipschitz classes $Lip^{(p)}α(W) (1 ≥ p ≥ ∞, α > 0)$ 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 $B^α_{p,q}$ 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 $B^α_{p,q}$ 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.
@article{10_4064_sm_110_2_127_148,
author = {Jun Tateoka},
title = {On the characterization of {Hardy-Besov} spaces on the dyadic group and its applications},
journal = {Studia Mathematica},
pages = {127--148},
publisher = {mathdoc},
volume = {110},
number = {2},
year = {1994},
doi = {10.4064/sm-110-2-127-148},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-110-2-127-148/}
}
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Jun Tateoka. On the characterization of Hardy-Besov spaces on the dyadic group and its applications. Studia Mathematica, Tome 110 (1994) no. 2, pp. 127-148. doi: 10.4064/sm-110-2-127-148
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