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Multiplier theorems for Herz type Hardy spaces

Author(s): Shanzhen Lu; Dachun Yang
Journal: Proc. Amer. Math. Soc. 126 (1998), 3337-3346.
MSC (1991): Primary 42B15; Secondary 42B30
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Abstract | References | Similar articles | Additional information

Abstract: In this paper, the authors establish a multiplier theorem for Herz type Hardy spaces.

References:

[BS]
A. Baernstein II and E. T. Sawyer, Embedding and Multiplier Theorem for $H^{p}(\mathbb{R}^{n})$, Memoirs of Amer. Math. Soc., vol. 53, no. 318, Amer. Math. Soc., Providence R. I., 1985. MR 86g:42036

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Y. Z. Chen and K. S. Lau, On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278. MR 90f:46059

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R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 56:6264

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C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. MR 56:6263

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J. García-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), 499-513. MR 90i:42032

[LY1]
S. Z. Lu and D. C. Yang, The Littlewood-Paley function and $\varphi $-transform characterizations of a new Hardy space $HK_{2}$ associated with the Herz space, Studia Math. 101 (1992), 285-298. MR 93b:42031

[LY2]
S. Z. Lu and D. C. Yang, The decomposition of the weighted Herz spaces on $\mathbb{R}^{n}$ and its applications, Sci. in China (Ser. A) 38 (1995), 147-158. MR 96c:46026

[LY3]
S. Z. Lu and D. C. Yang, The weighted Herz-type Hardy space and its applications, Sci. in China (Ser. A) 38 (1995), 662-673. MR 96i:42018

[Y]
D. C. Yang, Some Hardy Spaces Associated with the Herz Spaces, Doctoral Dissertation, Beijing Normal University, Beijing, 1992.

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Additional Information:

Shanzhen Lu
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China
Email: lusz@bnu.edu.cn

Dachun Yang
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China
Email: dcyang@bnu.edu.cn

DOI: 10.1090/S0002-9939-98-04931-4
PII: S 0002-9939(98)04931-4
Keywords: Herz space, Hardy space, multiplier
Received by editor(s): April 13, 1995
Received by editor(s) in revised form: April 5, 1997
Additional Notes: Research was supported by NNSF and SEDF of China.
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1998, American Mathematical Society

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