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Hörmander condition for pseudo-multipliers associated to the harmonic oscillator (1810.01260v1)
Published 2 Oct 2018 in math.FA, math.AP, and math.SP
Abstract: In this paper we prove H\"ormander-Mihlin multiplier theorems for pseudo-multipliers associated to the harmonic oscillator (also called the Hermite operator). Our approach can be extended to also obtain the $Lp$-boundedness results for multilinear pseudo-multipliers. By using the Littlewood-Paley theorem associated to the harmonic oscillator we also give $Lp$-boundedness and $Lp$-compactness properties for multipliers. $(Lp,Lq)$-estimates for spectral pseudo-multipliers also are investigated.