Nikolskii inequality and besov, triebel-lizorkin, wiener and beurling spaces on compact homogeneous manifolds

Erlan Nursultanov, Michael Ruzhansky, Sergey Tikhonov

    Research output: Contribution to journalArticleResearchpeer-review

    14 Citations (Scopus)

    Abstract

    In this paper we prove Nikolskii's inequality (also known as the reverse Hölder inequality) on general compact Lie groups and on compact homogeneous spaces with the constant interpreted in terms of the eigenvalue counting function of the Laplacian on the space, giving the best constant for certain indices, attained on the Dirichlet kernel. Consequently, we establish embedding theorems between Besov spaces on compact homogeneous spaces, as well as em- beddings between Besov spaces and Wiener and Beurling spaces. We also analyse Triebel-Lizorkin spaces and β-versions of Wiener and Beurling spaces and their embeddings, and interpolation properties of all these spaces.
    Original languageEnglish
    Pages (from-to)981-1017
    JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
    Volume16
    Issue number3
    Publication statusPublished - 1 Jan 2016

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