The generalized localization for multiple Fourier integrals.
In this paper we investigate almost-everywhere convergence properties of the Bochner–Riesz means of N-fold Fourier integrals under summation over domains bounded by the level surfaces of the elliptic polynomials. It is proved that if the order of the Bochner–Riesz means s⩾(N−1)(1/p−1/2), then the Bo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Academic Press Inc.
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17168/1/The%20generalized%20localization%20for%20multiple%20Fourier%20integrals.pdf http://psasir.upm.edu.my/id/eprint/17168/ |
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| Summary: | In this paper we investigate almost-everywhere convergence properties of the Bochner–Riesz means of N-fold Fourier integrals under summation over domains bounded by the level surfaces of the elliptic polynomials. It is proved that if the order of the Bochner–Riesz means s⩾(N−1)(1/p−1/2), then the Bochner–Riesz means of a function f∈Lp(RN), 1⩽p⩽2 converge to zero almost-everywhere on RN∖supp(f). |
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