Móricz Ferenc honlapja

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Cím:A new characterization of Besov spaces on the real line.
Szerző:Giang, Dang Vu; M\'oricz, Ferenc
Forrás:J. Math. Anal. Appl. 189, No.2, 533-551 (1995).
Nyelv:English
Absztrakt:The authors give a new characterization of functions $f$ defined on the real line $(-\infty, \infty)$ in order to belong to a Besov space $B\sp{p, r}\sb \alpha$ for some $0< \alpha< 1$ and $1\le p$, $r\le \infty$. These conditions are in terms of the Riesz mean of $f$ in case $1\le p\le \infty$, and in terms of the Dirichlet integral of $f$ in case $1< p< \infty$. An analogous characterization of periodic functions on the torus $[-\pi, \pi)$ was initiated by Fourier and Self, via the partial sums of their Fourier series. The novelty in the authors' treatment is that they use norms involving integrals, instead of norms involving sums of infinite series. Their approach is also appropriate to building up a complete characterization of Besov spaces on the torus. 
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