The Journal of Geometric Analysis

, Volume 29, Issue 2, pp 1571–1582 | Cite as

A Plancherel–Polya Inequality in Besov Spaces on Spaces of Homogeneous Type

  • Philippe JamingEmail author
  • Felipe Negreira


In this work, we establish a Plancherel–Polya inequality for functions in Besov spaces on spaces of homogeneous type as defined in Han and Yang (Diss Math 403:1–102, 2002) in the spirit of their recent counterpart for \({\mathbb {R}}^d\) established by Jaming and Malinnikova (J Fourier Anal Appl 22:768–786, 2016. The main tool is the wavelet decomposition presented by Deng and Han (Harmonic Analysis on Spaces of Homogeneous Type, Springer, New York, 2009).


Besov spaces Sampling theory Plancherel–Polya inequality Spaces of homogeneous type 

Mathematics Subject Classification

Primary 94A20 Secondary 30H25 43A85 



The authors wish to thank the anonymous referees for a careful reading of the manuscript and constructive remarks. The first author kindly acknowledges the financial support from the French ANR program, ANR-12-BS01-0001 (Aventures), the Austrian-French AMA-DEUS project 35598VB-ChargeDisq, and the French-Tunisian CMCU/UTIQUE project 32701UB Popart. This study has been carried out with the financial support from the French State, managed by the French National Research Agency (ANR) in the framework of the Investments for the Future Program IdEx Bordeaux—CPU (ANR-10-IDEX-03-02). The second author is supported by the doctoral grant POS-CFRA-2015-1-125008 of the Agencia Nacional de Innovación e Investigación (Uruguay) and the Campus France (France).


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© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Univ. Bordeaux, IMB, CNRS, UMR 5251TalenceFrance

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