A note on restricted weak-type estimates for bochner-riesz operators with negative index in ℝd, n ≥ 2

Susana Gutiérrez

doi:10.1090/s0002-9939-99-05144-8

A note on restricted weak-type estimates for bochner-riesz operators with negative index in ℝ^d, n ≥ 2

Susana Gutiérrez^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown that the Bochner-Riesz operator on ℝ^d of negative order a is of restricted weak type in the critical points (p₀, q₀) and (q′₀,p′₀), where 1/q₀ = 3/4 + α/2, q₀ = p′₀/3 for -3/2 < α α 0 in the two-dimensional case and l/q₀ = (n + 1 + 2α)/2n, q₀ = (n - 1)p′₀/(n + 1), for -(n + 1)/2 < α < -1/2 if n ≥ 3.

Original language	English
Pages (from-to)	495-501
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	128
Issue number	2
DOIs	https://doi.org/10.1090/s0002-9939-99-05144-8
Publication status	Published - 2000

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-99-05144-8

Cite this

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title = "A note on restricted weak-type estimates for bochner-riesz operators with negative index in ℝd, n ≥ 2",

abstract = "It is shown that the Bochner-Riesz operator on ℝd of negative order a is of restricted weak type in the critical points (p0, q0) and (q′0,p′0), where 1/q0 = 3/4 + α/2, q0 = p′0/3 for -3/2 < α α 0 in the two-dimensional case and l/q0 = (n + 1 + 2α)/2n, q0 = (n - 1)p′0/(n + 1), for -(n + 1)/2 < α < -1/2 if n ≥ 3.",

author = "Susana Guti{\'e}rrez",

year = "2000",

doi = "10.1090/s0002-9939-99-05144-8",

language = "English",

volume = "128",

pages = "495--501",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

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T1 - A note on restricted weak-type estimates for bochner-riesz operators with negative index in ℝd, n ≥ 2

AU - Gutiérrez, Susana

PY - 2000

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N2 - It is shown that the Bochner-Riesz operator on ℝd of negative order a is of restricted weak type in the critical points (p0, q0) and (q′0,p′0), where 1/q0 = 3/4 + α/2, q0 = p′0/3 for -3/2 < α α 0 in the two-dimensional case and l/q0 = (n + 1 + 2α)/2n, q0 = (n - 1)p′0/(n + 1), for -(n + 1)/2 < α < -1/2 if n ≥ 3.

AB - It is shown that the Bochner-Riesz operator on ℝd of negative order a is of restricted weak type in the critical points (p0, q0) and (q′0,p′0), where 1/q0 = 3/4 + α/2, q0 = p′0/3 for -3/2 < α α 0 in the two-dimensional case and l/q0 = (n + 1 + 2α)/2n, q0 = (n - 1)p′0/(n + 1), for -(n + 1)/2 < α < -1/2 if n ≥ 3.

UR - https://www.scopus.com/pages/publications/22844456690

U2 - 10.1090/s0002-9939-99-05144-8

DO - 10.1090/s0002-9939-99-05144-8

M3 - Article

AN - SCOPUS:22844456690

SN - 0002-9939

VL - 128

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EP - 501

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2