Lp - Lq bounds for spherical maximal operators

T. Anderson; K. Hughes; J. Roos; A. Seeger

doi:10.1007/s00209-020-02546-0

Lp - Lq bounds for spherical maximal operators

T. Anderson, K. Hughes, J. Roos, A. Seeger^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

22 Citations (Scopus)

Abstract

Let f∈Lp(Rd), d≥3, and let Atf(x) the average of f over the sphere with radius t centered at x. For a subset E of [1,2] we prove close to sharp Lp→Lq estimates for the maximal function supt∈E|Atf|. A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result can be applied to prove sparse domination bounds for a related global spherical maximal function.

Original language	English
Pages (from-to)	1057-1074
Journal	Mathematische Zeitschrift
Volume	297
Issue number	3-4
Early online date	5 Jun 2020
DOIs	https://doi.org/10.1007/s00209-020-02546-0
Publication status	Published - 1 Apr 2021

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https://arxiv.org/abs/1909.05389

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title = "Lp - Lq bounds for spherical maximal operators",

abstract = "Let f∈Lp(Rd), d≥3, and let Atf(x) the average of f over the sphere with radius t centered at x. For a subset E of [1,2] we prove close to sharp Lp→Lq estimates for the maximal function supt∈E|Atf|. A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result can be applied to prove sparse domination bounds for a related global spherical maximal function.",

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T1 - Lp - Lq bounds for spherical maximal operators

AU - Anderson, T.

AU - Hughes, K.

AU - Roos, J.

AU - Seeger, A.

PY - 2021/4/1

Y1 - 2021/4/1

N2 - Let f∈Lp(Rd), d≥3, and let Atf(x) the average of f over the sphere with radius t centered at x. For a subset E of [1,2] we prove close to sharp Lp→Lq estimates for the maximal function supt∈E|Atf|. A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result can be applied to prove sparse domination bounds for a related global spherical maximal function.

AB - Let f∈Lp(Rd), d≥3, and let Atf(x) the average of f over the sphere with radius t centered at x. For a subset E of [1,2] we prove close to sharp Lp→Lq estimates for the maximal function supt∈E|Atf|. A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result can be applied to prove sparse domination bounds for a related global spherical maximal function.

U2 - 10.1007/s00209-020-02546-0

DO - 10.1007/s00209-020-02546-0

M3 - Article (Academic Journal)

SN - 0025-5874

VL - 297

SP - 1057

EP - 1074

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Lp - Lq bounds for spherical maximal operators

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