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On multipliers for \(\text{BMO}_ \phi\) on general domains. (English) Zbl 0809.42003
In a previous paper [Kodai Math. J. 16, No. 1, 79-89 (1993; Zbl 0783.42014)]the author characterized the class of pointwise multipliers on \(\text{BMO}(D)\), for a domain \(D\subset \mathbb{R}^ d\) [for the case \(D= \mathbb{R}^ n\) see S. Janson’s article in Ark. Mat. 14, 189-196 (1976; Zbl 0341.43005)]. In the present paper this characterization is extended to a class \(\text{BMO}_{\phi,p}(D)\), consisting of \(L^ p_{\text{loc}}\)-functions satisfying the condition \(\sup_{Q\in D}(\phi(l(Q)))^{-1}\bigl(m(Q)^{-1}\int_ Q | f- f_ Q|^ p dx\bigr)^{1/p}< \infty\), for suitable \(\phi\).
Reviewer: A.Seeger (Madison)

MSC:
42B15 Multipliers for harmonic analysis in several variables
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