Some remarks on Bochner-Riesz means

S. Thangavelu

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 2, page 217-230
  • ISSN: 0010-1354

Abstract

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We study L p norm convergence of Bochner-Riesz means S R δ f associated with certain non-negative differential operators. When the kernel S R m ( x , y ) satisfies a weak estimate for large values of m we prove L p norm convergence of S R δ f for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.

How to cite

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Thangavelu, S.. "Some remarks on Bochner-Riesz means." Colloquium Mathematicae 83.2 (2000): 217-230. <http://eudml.org/doc/210783>.

@article{Thangavelu2000,
abstract = {We study $L^p$ norm convergence of Bochner-Riesz means $S_R^δ f$ associated with certain non-negative differential operators. When the kernel $S_R^m(x,y)$ satisfies a weak estimate for large values of m we prove $L^p$ norm convergence of $S_R^δ f$ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.},
author = {Thangavelu, S.},
journal = {Colloquium Mathematicae},
keywords = {unitary representations; Schrödinger operators; Bochner-Riesz means; nilpotent groups; Rockland operators; Heisenberg group; summability; spectral resolution},
language = {eng},
number = {2},
pages = {217-230},
title = {Some remarks on Bochner-Riesz means},
url = {http://eudml.org/doc/210783},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Thangavelu, S.
TI - Some remarks on Bochner-Riesz means
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 2
SP - 217
EP - 230
AB - We study $L^p$ norm convergence of Bochner-Riesz means $S_R^δ f$ associated with certain non-negative differential operators. When the kernel $S_R^m(x,y)$ satisfies a weak estimate for large values of m we prove $L^p$ norm convergence of $S_R^δ f$ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.
LA - eng
KW - unitary representations; Schrödinger operators; Bochner-Riesz means; nilpotent groups; Rockland operators; Heisenberg group; summability; spectral resolution
UR - http://eudml.org/doc/210783
ER -

References

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