Averaging operators along a certain type of surfaces with hypersingularity

Jin Bong Lee; Jongho Lee; Chan Woo Yang

doi:10.11650/tjm/191101

Averaging operators along a certain type of surfaces with hypersingularity

Jin Bong Lee, Jongho Lee, Chan Woo Yang

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

Abstract

In this paper we obtain almost sharp decay estimates for L² operator norm of strongly singular oscillatory integral operators in ℝⁿ⁺¹ for n ≥ 2; we prove some necessary condition for L² estimates. Also, we prove that the operators are bounded on L^p for some p ≠ 2 and the range of p depends on the hypersingularity of the operators.

Original language	English
Pages (from-to)	317-329
Number of pages	13
Journal	Taiwanese Journal of Mathematics
Volume	24
Issue number	2
DOIs	https://doi.org/10.11650/tjm/191101
Publication status	Published - 2020 Apr

Bibliographical note

Publisher Copyright:
© 2020, Mathematical Society of the Rep. of China. All rights reserved.

Keywords

Bessel
Functions
Hypersingularity
Oscillatory integrals
Singular integrals along surfaces

ASJC Scopus subject areas

General Mathematics

Access to Document

10.11650/tjm/191101

Cite this

@article{f64280a42f11488b82db51b7303b2e52,

title = "Averaging operators along a certain type of surfaces with hypersingularity",

abstract = "In this paper we obtain almost sharp decay estimates for L2 operator norm of strongly singular oscillatory integral operators in ℝn+1 for n ≥ 2; we prove some necessary condition for L2 estimates. Also, we prove that the operators are bounded on Lp for some p ≠ 2 and the range of p depends on the hypersingularity of the operators.",

keywords = "Bessel, Functions, Hypersingularity, Oscillatory integrals, Singular integrals along surfaces",

author = "Lee, {Jin Bong} and Jongho Lee and Yang, {Chan Woo}",

year = "2020",

month = apr,

doi = "10.11650/tjm/191101",

language = "English",

volume = "24",

pages = "317--329",

journal = "Taiwanese Journal of Mathematics",

issn = "1027-5487",

publisher = "Mathematical Society of the Rep. of China",

number = "2",

}

TY - JOUR

T1 - Averaging operators along a certain type of surfaces with hypersingularity

AU - Lee, Jin Bong

AU - Lee, Jongho

AU - Yang, Chan Woo

PY - 2020/4

Y1 - 2020/4

N2 - In this paper we obtain almost sharp decay estimates for L2 operator norm of strongly singular oscillatory integral operators in ℝn+1 for n ≥ 2; we prove some necessary condition for L2 estimates. Also, we prove that the operators are bounded on Lp for some p ≠ 2 and the range of p depends on the hypersingularity of the operators.

AB - In this paper we obtain almost sharp decay estimates for L2 operator norm of strongly singular oscillatory integral operators in ℝn+1 for n ≥ 2; we prove some necessary condition for L2 estimates. Also, we prove that the operators are bounded on Lp for some p ≠ 2 and the range of p depends on the hypersingularity of the operators.

KW - Bessel

KW - Functions

KW - Hypersingularity

KW - Oscillatory integrals

KW - Singular integrals along surfaces

UR - http://www.scopus.com/inward/record.url?scp=85082722847&partnerID=8YFLogxK

U2 - 10.11650/tjm/191101

DO - 10.11650/tjm/191101

M3 - Article

AN - SCOPUS:85082722847

SN - 1027-5487

VL - 24

SP - 317

EP - 329

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

IS - 2

ER -

Averaging operators along a certain type of surfaces with hypersingularity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this