Bochner-Riesz means for the Hermite and special Hermite expansions

Sanghyuk Lee; Jaehyeon Ryu

doi:10.1016/j.aim.2022.108260

Bochner-Riesz means for the Hermite and special Hermite expansions

Sanghyuk Lee, Jaehyeon Ryu

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

6 Scopus citations

Abstract

We consider the Bochner-Riesz means for the Hermite and special Hermite expansions. Developing further Thangavelu's approach [31], we study their L^p boundedness with the sharp summability index in a local setting. In two dimensions we establish the boundedness on the optimal range of p and extend the previously known range in higher dimensions. Furthermore, we prove a new lower bound on the L^p summability index for the Hermite Bochner-Riesz means in R^d, d≥2. This invalidates the conventional conjecture which was expected to be true.

Original language	English
Article number	108260
Journal	Advances in Mathematics
Volume	400
DOIs	https://doi.org/10.1016/j.aim.2022.108260
State	Published - 14 May 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Bochner-Riesz means
Hermite and special Hermite functions

Access to Document

10.1016/j.aim.2022.108260

Cite this

@article{17328273408648b5809e6a32bf4c8aba,

title = "Bochner-Riesz means for the Hermite and special Hermite expansions",

abstract = "We consider the Bochner-Riesz means for the Hermite and special Hermite expansions. Developing further Thangavelu's approach [31], we study their Lp boundedness with the sharp summability index in a local setting. In two dimensions we establish the boundedness on the optimal range of p and extend the previously known range in higher dimensions. Furthermore, we prove a new lower bound on the Lp summability index for the Hermite Bochner-Riesz means in Rd, d≥2. This invalidates the conventional conjecture which was expected to be true.",

keywords = "Bochner-Riesz means, Hermite and special Hermite functions",

author = "Sanghyuk Lee and Jaehyeon Ryu",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = may,

day = "14",

doi = "10.1016/j.aim.2022.108260",

language = "English",

volume = "400",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Bochner-Riesz means for the Hermite and special Hermite expansions

AU - Lee, Sanghyuk

AU - Ryu, Jaehyeon

PY - 2022/5/14

Y1 - 2022/5/14

N2 - We consider the Bochner-Riesz means for the Hermite and special Hermite expansions. Developing further Thangavelu's approach [31], we study their Lp boundedness with the sharp summability index in a local setting. In two dimensions we establish the boundedness on the optimal range of p and extend the previously known range in higher dimensions. Furthermore, we prove a new lower bound on the Lp summability index for the Hermite Bochner-Riesz means in Rd, d≥2. This invalidates the conventional conjecture which was expected to be true.

AB - We consider the Bochner-Riesz means for the Hermite and special Hermite expansions. Developing further Thangavelu's approach [31], we study their Lp boundedness with the sharp summability index in a local setting. In two dimensions we establish the boundedness on the optimal range of p and extend the previously known range in higher dimensions. Furthermore, we prove a new lower bound on the Lp summability index for the Hermite Bochner-Riesz means in Rd, d≥2. This invalidates the conventional conjecture which was expected to be true.

KW - Bochner-Riesz means

KW - Hermite and special Hermite functions

UR - https://www.scopus.com/pages/publications/85125128408

U2 - 10.1016/j.aim.2022.108260

DO - 10.1016/j.aim.2022.108260

M3 - Article

AN - SCOPUS:85125128408

SN - 0001-8708

VL - 400

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108260

ER -

Bochner-Riesz means for the Hermite and special Hermite expansions

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this