A note on iterated spherical average on Lebesgue spaces

A note on iterated spherical average on Lebesgue spaces

For the spherical average A and the Laplace operator Δ, we study the iterated operator ΔAN and find the minimal positive integer N to ensure the L1Rn boundedness of ΔAN. Using a constructive proof, we completely solve a question posted by Belinsky et al. (2003).

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Veröffentlicht in:Nonlinear analysis 2019-03, Vol.180, p.170-183
Hauptverfasser: Fan, Dashan, Lou, Zengjian, Wang, Zijian
Format: Artikel
Sprache:eng
Schlagworte:
Bessel functions
K-functional
Spherical average
Wave operator
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Zusammenfassung:For the spherical average A and the Laplace operator Δ, we study the iterated operator ΔAN and find the minimal positive integer N to ensure the L1Rn boundedness of ΔAN. Using a constructive proof, we completely solve a question posted by Belinsky et al. (2003).
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2018.10.004