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Pointwise Convergence of Bochner–Riesz Means in Sobolev Spaces
2013The Bochner–Riesz means are defined by the Fourier multiplier operators \((S_{R}^{\alpha}\ast f)\hat{\ }(\xi)=( 1-|R^{-1} \xi|^{2})^{\alpha}_{+}\hat{f}(\xi)\). Here we prove that if f has β derivatives in L p (R d ), then \(S_{R}^{\alpha}\ast f(x)\) converges pointwise to f(x) as R→+∞ with a possible exception of a set of points with Hausdorff ...
Colzani, L, Volpi, SM
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Approximation for spherical functions by Bochner-Riesz means
Approximation Theory and its Applications, 1991Let \(\Sigma_ n\) be the unit sphere in the \((n+1)\)-dimensional Euclidean space, \(f\in L^ p(\Sigma_ n)\) for some \(1\leq p\leq \infty\), \(f(u)\sim\sum^ \infty_{k=0} Y_ k(f;u)\) the Fourier-Laplace series of \(f\), and \[ S^ \delta_ R(f;u):=\sum_{k0, R>0, \] its Bochner- Riesz mean.
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Strong Uniform Approximation by Bochner-Riesz Means
1989All those real-valued continuous functions defined on Rn which are periodic in each variable with period 2π compose a Banach space with max-norm.
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Localization of the Bochner-Riesz means in the Nikol'skii classes
Ukrainian Mathematical Journal, 1993The author proved five theorems presenting conditions for localization of the Bochner-Riesz means in the Nikol'skij classes.
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Generalized Bochner-Riesz Means of Fourier Integrals
1989In this paper, almost everywhere approximation order to a function in Bessel Potential space by generalized Bochner-Riesz means is given.
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On almost everywhere summability of conjugate Bochner-Riesz means
Approximation Theory and its Applications, 2000In this paper the author discusses the conjugate Bochner-Riesz means of functions in \(L^p({\mathbb R}^n)\) with ...
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Quasiradial Bochner-Riesz means for some nonsmooth distance functions
Indiana University Mathematics Journal, 1997The author considers convergence of some quasiradial Bochner-Riesz means defined as \({\mathfrak R}^\delta_{\rho,t}f=F^{-1}[(1-\rho/t)^\delta_+\hat{f}]\), in the 2-dimensional case where \(\rho=| \xi_1| ^{\alpha_1}+ | \xi_2| ^{\alpha_2}\). To do this he studies weak-\((1,1)\) estimate for the maximal operator \(M^\delta_\rho=\sup_{t>0} | {\mathfrak R}^\
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A Weighted Maximal L2 Estimate of Operator-valued Bochner–Riesz Means
Acta Mathematica Sinica, English SerieszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong, Guixiang, Zhang, Liyuan
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Bounds on the maximal Bochner-Riesz means for elliptic operators
Transactions of the American Mathematical Society, 2020Peng Chen, Adam Sikora
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