Plancherel-type estimates and sharp spectral multipliers

Xuan Thinh Duong, El Maati Ouhabaz, Adam Sikora*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    133 Citations (Scopus)

    Abstract

    We study general spectral multiplier theorems for self-adjoint positive definite operators on L2 (X, μ), where X is any open subset of a space of homogeneous type. We show that the sharp Hörmander-type spectral multiplier theorems follow from the appropriate estimates of the L2 norm of the kernel of spectral multipliers and the Gaussian bounds for the corresponding heat kernel The sharp Hörmander-type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the Riesz means summability, which we also study here. We discuss several examples, which include sharp spectral multiplier theorems for a class of scattering operators on R3 and new spectral multiplier theorems for the Laguerre and Hermite expansions.

    Original languageEnglish
    Pages (from-to)443-485
    Number of pages43
    JournalJournal of Functional Analysis
    Volume196
    Issue number2
    DOIs
    Publication statusPublished - 20 Dec 2002

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