Pointwise multipliers of weighted BMO spaces

Author:
Kôzô Yabuta

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

MSC:
Primary 42B15

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

MathSciNet review:
1123671

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Abstract | References | Similar Articles | Additional Information

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]**S. Bloom,*Pointwise multipliers of weighted**spaces*, Proc. Amer. Math. Soc.**105**(1989), 950-960. MR**960640 (90c:42013)****[2]**R. R. Coifman and G. Weiss,*Extensions of Hardy spaces and their use in analysis*, Bull. Amer. Math. Soc.**83**(1977), 569-645. MR**0447954 (56:6264)****[3]**E. Nakai,*Pointwise multipliers for functions of weighted bounded mean oscillation*, Studia Math, (to appear). MR**1226621 (94h:42026)****[4]**E. Nakai and K. Yabuta,*Pointwise multipliers for functions of bounded mean oscillation*, J. Math. Soc. Japan**37**(1985), 207-218. MR**780660 (87d:42020)****[5]**J.-O. Strömberg and A. Torchinsky,*Weighted Hardy spaces*, Lecture Notes in Math., vol. 1381, Springer-Verlag, Berlin and Heidelberg, 1989. MR**1011673 (90j:42053)****[6]**A. Uchiyama, Lecture notes (285I), Department of Mathematics, University of California, Los Angeles, 1980-1981.

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Additional Information

DOI:
https://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