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

Abstract

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).