Oscillating singular integral operators on compact Lie groups revisited
نویسندگان
چکیده
Abstract Fefferman (Acta Math 24:9–36, 1970, Theorem 2 $$'$$ ′ ) has proved the weak (1,1) boundedness for a class of oscillating singular integrals that includes spectral multipliers Euclidean Laplacian $$\Delta ,$$ Δ , namely, operators form $$\begin{aligned} T_{\theta }(-\Delta ):= (1-\Delta )^{-\frac{n\theta }{4}}e^{i )^{\frac{\theta }{2}}},\,0\le \theta <1. \end{aligned}$$ T θ ( - ) : = 1 n 4 e i 2 0 ≤ < . The aim this work is to extend Fefferman’s result on any arbitrary compact Lie group. We also consider applications Laplace–Beltrami operator. proof our main theorem illustrates delicate relationship between condition kernel operator, its Fourier transform (defined in terms representation theory group) and microlocal/geometric properties
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2022
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-022-03175-5