CIRCULAR AVERAGE RELATIVE TO FRACTAL MEASURES

Seheon Ham; Hyerim Ko; Sanghyuk Lee

doi:10.3934/cpaa.2022100

CIRCULAR AVERAGE RELATIVE TO FRACTAL MEASURES

Seheon Ham
, Hyerim Ko^*
, Sanghyuk Lee

^*Corresponding author for this work

Department of Mathematics

Seoul National University

Research output: Contribution to journal › Journal article › peer-review

5 Scopus citations

Abstract

We prove new Lp-Lq estimates for averages over dilates of the circle with respect to fractal measures, which unify different types of maximal estimates for the circular average. Our results are consequences of Lp-Lq smoothing estimates for the wave operator relative to fractal measures. We also discuss similar results concerning the spherical averages.

Original language	English
Pages (from-to)	3283-3307
Number of pages	25
Journal	Communications on Pure and Applied Analysis
Volume	21
Issue number	10
DOIs	https://doi.org/10.3934/cpaa.2022100
State	Published - 2022.10

Keywords

circular average
general measures

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10.3934/cpaa.2022100

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title = "CIRCULAR AVERAGE RELATIVE TO FRACTAL MEASURES",

abstract = "We prove new Lp-Lq estimates for averages over dilates of the circle with respect to fractal measures, which unify different types of maximal estimates for the circular average. Our results are consequences of Lp-Lq smoothing estimates for the wave operator relative to fractal measures. We also discuss similar results concerning the spherical averages.",

keywords = "circular average, general measures",

author = "Seheon Ham and Hyerim Ko and Sanghyuk Lee",

year = "2022",

month = oct,

doi = "10.3934/cpaa.2022100",

language = "English",

volume = "21",

pages = "3283--3307",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

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TY - JOUR

T1 - CIRCULAR AVERAGE RELATIVE TO FRACTAL MEASURES

AU - Ham, Seheon

AU - Ko, Hyerim

AU - Lee, Sanghyuk

PY - 2022/10

Y1 - 2022/10

N2 - We prove new Lp-Lq estimates for averages over dilates of the circle with respect to fractal measures, which unify different types of maximal estimates for the circular average. Our results are consequences of Lp-Lq smoothing estimates for the wave operator relative to fractal measures. We also discuss similar results concerning the spherical averages.

AB - We prove new Lp-Lq estimates for averages over dilates of the circle with respect to fractal measures, which unify different types of maximal estimates for the circular average. Our results are consequences of Lp-Lq smoothing estimates for the wave operator relative to fractal measures. We also discuss similar results concerning the spherical averages.

KW - circular average

KW - general measures

UR - https://www.scopus.com/pages/publications/85136286106

U2 - 10.3934/cpaa.2022100

DO - 10.3934/cpaa.2022100

M3 - Journal article

AN - SCOPUS:85136286106

SN - 1534-0392

VL - 21

SP - 3283

EP - 3307

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 10

ER -

CIRCULAR AVERAGE RELATIVE TO FRACTAL MEASURES

Abstract

Keywords

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