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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Plancherel-Pôlya type inequality on spaces of homogeneous type and its applications
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by Y.-S. Han PDF
Proc. Amer. Math. Soc. 126 (1998), 3315-3327 Request permission

Abstract:

In this paper, using the discrete Calderon reproducing formula on spaces of homogeneous type obtained by the author, we obtain the Plancherel-Pôlya type inequalities on spaces of homogeneous type. These inequalities give new characterizations of the Besov spaces $\dot B_p^{\alpha ,q}$ and the Triebel-Lizorkin spaces $\dot F_p^{\alpha ,q}$ on spaces of homogeneous type introduced earlier by the author and E. T. Sawyer and also allow us to generalize these spaces to the case where $p,q\le 1$. Moreover, using these inequalities, we can easily show that the Littlewood-Paley $G$-function and $S$-function are equivalent on spaces of homogeneous type, which gives a new characterization of the Hardy spaces on spaces of homogeneous type introduced by Macias and Segovia.
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Additional Information
  • Y.-S. Han
  • Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849-5310
  • MR Author ID: 209888
  • Email: hanyong@mail.auburn.edu
  • Received by editor(s): September 19, 1996
  • Received by editor(s) in revised form: April 1, 1997
  • Communicated by: J. Marshall Ash
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3315-3327
  • MSC (1991): Primary 42B25, 46F05
  • DOI: https://doi.org/10.1090/S0002-9939-98-04445-1
  • MathSciNet review: 1459123