Abstract
In this paper, we characterize the symbol in Hormander symbol classS mρ ,δ (m ∈ R, ρ, δ ≥ 0) by its wavelet coefficients. Consequently, we analyse the kerneldistribution property for the symbol in the symbol classS mρ ,δ (m ∈R, ρ > 0, δ≥ 0) which is more general than known results ; for non-regular symbol operators, we establish sharp L2-continuity which is better than Calderón and Vaillancourt’s result, and establishL p (1 ≤p ≤∞) continuity which is new and sharp. Our new idea is to analyse the symbol operators in phase space with relative wavelets, and to establish the kernel distribution property and the operator’s continuity on the basis of the wavelets coefficients in phase space.
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Yang, Q.X. Wavelet characterization of Hörmander symbol classS mρ,δ and applications. Proc Math Sci 115, 347–368 (2005). https://doi.org/10.1007/BF02829664
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DOI: https://doi.org/10.1007/BF02829664