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Classic and Exotic Besov Spaces Induced by Good Grids

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Abstract

In a previous work we introduced Besov spaces \({\mathcal {B}}^s_{p,q}\) defined on a measure space with a good grid, with \(p\in [1,\infty )\), \(q\in [1,\infty ]\) and \(0< s< 1/p\). Here we show that classical Besov spaces on compact homogeneous spaces are examples of such Besov spaces. On the other hand we show that even Besov spaces defined by a good grid made of partitions by intervals may differ from a classical Besov space, giving birth to exotic Besov spaces.

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  1. Departamento de Matemática, Intituto de Ciências Matemáticas e da Computação-Universidade de São Paulo (ICMC/USP) - São Carlos, Caixa Postal 668, São Carlos, SP, CEP 13560-970, Brazil

    Daniel Smania

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Correspondence to Daniel Smania.

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D.S. was partially supported by CNPq 307617/2016-5, CNPq 430351/2018-6, CNPq 306622/2019-0 and FAPESP Projeto Temático 2017/06463-3.

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Smania, D. Classic and Exotic Besov Spaces Induced by Good Grids. J Geom Anal 31, 2481–2524 (2021). https://doi.org/10.1007/s12220-020-00361-x

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