Let Γ be the future light cone in ℝn, and Ω = ℝn + iΓ be the associated tube domain. We prove that the weighted Bergman projection Pv pvf(z) = ∫Ω f(w)Q(z - w̄)-vQ(script T signmw)v-ndw is bounded on Lp(Ω, Qv-n(script T signmw)dw) for 1 + n-2/2(v-1) < p < 1 + 2(v-1)/n-2, where Q denotes the Lorentz quadratic form. This theorem extends previous results by Bekollé and Bonami [BB]. Our proof relies on the analysis of the projection Pv, on mixed norm spaces, which allows us to exploit the oscillation of the Bergman kernel using the Laplace-Fourier transform.
Boundedness of Bergman projections on tube domains over light cones / D. Bekollé, A. Bonami, M.M. Peloso, F. Ricci. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 237:1(2001), pp. 31-59.
Boundedness of Bergman projections on tube domains over light cones
M.M. PelosoPenultimo
;
2001
Abstract
Let Γ be the future light cone in ℝn, and Ω = ℝn + iΓ be the associated tube domain. We prove that the weighted Bergman projection Pv pvf(z) = ∫Ω f(w)Q(z - w̄)-vQ(script T signmw)v-ndw is bounded on Lp(Ω, Qv-n(script T signmw)dw) for 1 + n-2/2(v-1) < p < 1 + 2(v-1)/n-2, where Q denotes the Lorentz quadratic form. This theorem extends previous results by Bekollé and Bonami [BB]. Our proof relies on the analysis of the projection Pv, on mixed norm spaces, which allows us to exploit the oscillation of the Bergman kernel using the Laplace-Fourier transform.File | Dimensione | Formato | |
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