Pointwise multipliers of weighted BMO spaces

Author:
Kôzô Yabuta

Journal:
Proc. Amer. Math. Soc. **117** (1993), 737-744

MSC:
Primary 42B15

MathSciNet review:
1123671

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Abstract: In a recent paper by S. Bloom (*Pointwise multipliers of weighted* *spaces*, Proc. Amer. Math. Soc. **105** (1989), 950-960), there are some inaccuracies. In this note, we give a counterexample to his "theorem" and a corrected form with proof under a suitable condition on weights. We also give some remarks and examples.

**[1]**Steven Bloom,*Pointwise multipliers of weighted BMO spaces*, Proc. Amer. Math. Soc.**105**(1989), no. 4, 950–960. MR**960640**, 10.1090/S0002-9939-1989-0960640-3**[2]**Ronald R. Coifman and Guido Weiss,*Extensions of Hardy spaces and their use in analysis*, Bull. Amer. Math. Soc.**83**(1977), no. 4, 569–645. MR**0447954**, 10.1090/S0002-9904-1977-14325-5**[3]**Eiichi Nakai,*Pointwise multipliers for functions of weighted bounded mean oscillation*, Studia Math.**105**(1993), no. 2, 105–119. MR**1226621****[4]**Eiichi Nakai and Kôzô Yabuta,*Pointwise multipliers for functions of bounded mean oscillation*, J. Math. Soc. Japan**37**(1985), no. 2, 207–218. MR**780660**, 10.2969/jmsj/03720207**[5]**Jan-Olov Strömberg and Alberto Torchinsky,*Weighted Hardy spaces*, Lecture Notes in Mathematics, vol. 1381, Springer-Verlag, Berlin, 1989. MR**1011673****[6]**A. Uchiyama, Lecture notes (285I), Department of Mathematics, University of California, Los Angeles, 1980-1981.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1123671-X

Keywords:
Pointwise multipliers,
weighted BMO,
BMO,
dyadic,
weighted Hardy spaces

Article copyright:
© Copyright 1993
American Mathematical Society