On the entropy norm spaces and the Hardy space

Author:
W. C. Lang

Journal:
Proc. Amer. Math. Soc. **118** (1993), 861-863

MSC:
Primary 42A16; Secondary 30D55, 42B30, 46E15

DOI:
https://doi.org/10.1090/S0002-9939-1993-1166359-1

MathSciNet review:
1166359

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Abstract | References | Similar Articles | Additional Information

Abstract: R. Dabrowski introduced certain natural multiplier operators which map from the entropy norm spaces of B. Korenblum into the Hardy space . We show that the images of the entropy norm spaces in do not include all of that space.

**[1]**R. Dabrowski,*Probability measure representation of norms associated with the notion of entropy*, Proc. Amer. Math. Soc.**90**(1984), 263-268. MR**727246 (86c:46020)****[2]**-,*On Fourier coefficients of a continuous periodic function of bounded entropy norm*, Bull. Amer. Math. Soc. (N.S.)**18**(1988), 49-51. MR**919659 (89b:42002)****[3]**-,*On a natural connection between the entropy spaces and Hardy space*, Proc. Amer. Math. Soc.**104**(1988), 812-818. MR**964862 (89m:42007)****[4]**B. Korenblum,*On a class of Banach spaces associated with the notion of entropy*, Trans. Amer. Math. Soc.**290**(1985), 527-553. MR**792810 (87a:46063)****[5]**W. C. Lang,*A growth condition for Fourier coefficients of a function of bounded entropy norm*, Proc. Amer. Math. Soc.**112**(1991), 433-439. MR**1045141 (91i:42005)****[6]**A. Zygmund,*Trigonometric series*, 2nd ed., vol. I, Cambridge Univ. Press, Cambridge, 1959. MR**0107776 (21:6498)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1166359-1

Keywords:
Entropy norm spaces,
real Hardy space

Article copyright:
© Copyright 1993
American Mathematical Society