riesz kernels
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2020 ◽  
Vol 26 (6) ◽  
Author(s):  
Reuben Wheeler

AbstractFor a general compact variety $$\Gamma $$ Γ of arbitrary codimension, one can consider the $$L^p$$ L p mapping properties of the Bochner–Riesz multiplier $$\begin{aligned} m_{\Gamma , \alpha }(\zeta ) \ = \ \mathrm{dist}(\zeta , \Gamma )^{\alpha } \phi (\zeta ) \end{aligned}$$ m Γ , α ( ζ ) = dist ( ζ , Γ ) α ϕ ( ζ ) where $$\alpha > 0$$ α > 0 and $$\phi $$ ϕ is an appropriate smooth cutoff function. Even for the sphere $$\Gamma = {{\mathbb {S}}}^{N-1}$$ Γ = S N - 1 , the exact $$L^p$$ L p boundedness range remains a central open problem in Euclidean harmonic analysis. In this paper we consider the $$L^p$$ L p integrability of the Bochner–Riesz convolution kernel for a particular class of varieties (of any codimension). For a subclass of these varieties the range of $$L^p$$ L p integrability of the kernels differs substantially from the $$L^p$$ L p boundedness range of the corresponding Bochner–Riesz multiplier operator.



2018 ◽  
Vol 43 ◽  
pp. 121-145 ◽  
Author(s):  
Bent Fuglede ◽  
Natalia Zorii
Keyword(s):  


2017 ◽  
Vol 291 (1) ◽  
pp. 55-85
Author(s):  
Helmut Harbrecht ◽  
Wolfgang L. Wendland ◽  
Natalia Zorii
Keyword(s):  






2011 ◽  
Vol 60 (4) ◽  
pp. 1319-1362 ◽  
Author(s):  
Joan Mateu ◽  
Laura Prat ◽  
Joan Verdera


2008 ◽  
Vol 14 (1) ◽  
pp. 16-38 ◽  
Author(s):  
Konstantin Runovski ◽  
Hans-Jürgen Schmeisser


2006 ◽  
Vol 134 (4) ◽  
pp. 2239-2257
Author(s):  
A. B. Aleksandrov
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