On the Bochner-Riesz means of critical order

Elijah Liflyand

Type: Article

Publication Date: 1997-01-01

Citations: 9

DOI: https://doi.org/10.1090/s0002-9939-97-03742-8

Abstract

Steinâs well-known logarithmic asymptotics of the Lebesgue constants of the Bochner-Riesz means of critical order is extended to Lebesgue constants of more general linear means of multiple Fourier series. These means are generated by certain class of functions supported in convex domains with boundaries of non-vanishing Gaussian curvature.

Locations

Proceedings of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	Lebesgue constants of Riesz type means of negative order	2021	Elijah Liflyand A. Podkorytov
+	Bochner–riesz Means On Euclidean Spaces	2013	Shanzhen Lu Dunyan Yan
+	Approximation Properties of Bochner-Riesz Means Below the Critical Index	1993	Shi Wang
+	Approximation Properties of Bochner-Riesz Means Below the Critical Index	1993	王时铭
+	On the almost everywhere convergence of Bochner-Riesz means of multiple Fourier series	1982	Shanzhen Lu Mitchell Taibleson Guido Weiss
+	ON THE CONVERGENCE OF RIESZ SPHERICAL MEANS OF MULTIPLE FOURIER SERIES AND INTEGRALS OF FUNCTIONS OF BOUNDED GENERALIZED VARIATION	1972	Б. И. Голубов
+	Approximation of Bochner-Riesz means of conjugate Fourier integrals below the critical index	1994	Shiming Wang
+ PDF Chat	The convergence of the Bochner-Riesz means at the critical index	1996	Lung-Kee Chen Dashan Fan
+ PDF Chat	The generalized localization for multiple Fourier integrals	2010	Ravshan Ashurov Anvarjon Ahmedov Ahmad Rodzi b. Mahmud
+	ON THE LOCALIZATION AND CONVERGENCE OF MULTIPLE FOURIER INTEGRAL BY BOCHNER-RIESZ MEANS	1993	Yū Maohe
+	On the localization and convergence of multiple Fourier integral by Bochner-Riesz means	1993	Yu Maohe
+	A note on the almost everywhere convergence of Bochner-Riesz means of multiple conjugate Fourier series	1982	Shanzhen Lu
+	Bochner–Riesz Means of Morrey Functions	2020	David R. Adams Jie Xiao
+	Estimates of Bochner-Martinelli integrals	2002	김신정
+	On the almost everywhere convergence of Bochner-Riesz of multiple Fourier series	1982	Guido Weiss Shanzhen Lu Mitchell Tableson
+ PDF Chat	Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series	1993	Luca Brandolini
+ PDF Chat	Riesz Means and Beurling Moving Averages	2019	Ν. H. Bingham
+ PDF Chat	Divergence of the Bochner-Riesz means in the weighted Hardy spaces	1996	Shūichi Satō
+	On the Convergence of Bochner-Riesz’s Spherical Means of Fourier Double Integrals	2021	M. G. ‎Grigoryan‎ L. S. Simonyan
+	On The Almost Everywhere Convergence Of Bochner-Riesz Means Of Multiple Fourier Integrals For Radial Functions	1992	Michitaka Kjima

Works That Cite This (9)

Action	Title	Year	Authors
+ PDF Chat	Some Recent Progress on the Restriction Conjecture	2004	Terence Tao
+	Lebesgue constants of Riesz type means of negative order	2021	Elijah Liflyand A. Podkorytov
+	One-Dimensional Fourier Transforms	2017	Ferenc Weisz
+	One-Dimensional Hardy Spaces	2017	Ferenc Weisz
+	Multi-Dimensional Hardy Spaces	2017	Ferenc Weisz
+	ℓ q -Summability of Multi-Dimensional Fourier Transforms	2017	Ferenc Weisz
+	Rectangular Summability of Multi-Dimensional Fourier Transforms	2017	Ferenc Weisz
+	Multi-Dimensional Fourier Transforms	2017	Ferenc Weisz
+	Lebesgue constants of multiple Fourier series	2006	Elijah Liflyand

Works Cited by This (9)

Action	Title	Year	Authors
+	Number of lattice points in families of homothetic domains in Rn	1983	Alexander Varchenko
+	Estimates from Below for Lebesgue Constants	1995	Elijah Liflyand А. Г. Рамм A.I. Zaslavsky
+ PDF Chat	𝐿^{𝑝} norms of certain kernels of the 𝑁-dimensional torus	1981	Leonardo Colzani Paolo M. Soardi
+ PDF Chat	Summation of multiple Fourier series by spherical means	1936	Salomon Bochner
+	On Certain Exponential Sums Arising In Multiple Fourier Series	1961	Elias M. Stein
+	L p Norms of Certain Kernels on the N-Dimensional Torus	1981	Leonardo Colzani Paolo M. Soardi
+	ON THE MEAN CONVERGENCE OF MULTIPLE FOURIER SERIES AND THE ASYMPTOTICS OF THE DIRICHLET KERNEL OF SPHERICAL MEANS	2018	K. I. Babenko
+ PDF Chat	Summation of Multiple Fourier Series by Spherical Means	1936	Salomon Bochner
+ PDF Chat	Singularities of the Radon transform	1993	А. Г. Рамм A.I. Zaslavsky