On dilation operators in Triebel-Lizorkin spaces
نویسندگان
چکیده
منابع مشابه
On dilation operators in Triebel-Lizorkin spaces
We consider dilation operators Tk : f → f(2 k ·) in the framework of Triebel-Lizorkin spaces F s p,q(R ). If s > n max ` 1 p − 1, 0 ́ , Tk is a bounded linear operator from F s p,q(R ) into itself and there are optimal bounds for its norm. We study the situation on the line s = n max ` 1 p − 1, 0 ́ , an open problem mentioned in [ET96, 2.3.1]. It turns out that the results shed new light upon the...
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Let T be the Calderón-Zygmund singular integral operator, a well-known result of Coifman et al. (see [6]) states that the commutator [b,T]( f ) = T(b f )− bT( f ) (where b ∈ BMO) is bounded on Lp(Rn) (1 < p <∞); Chanillo (see [1]) proves a similar result when T is replaced by the fractional integral operator; in [8, 9], these results on the TriebelLizorkin spaces and the case b ∈ Lipβ (where Li...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2009
ISSN: 0208-6573
DOI: 10.7169/facm/1261157806