Marstrand's Theorem revisited: projecting sets of dimension zero

Victor Beresnevich; Kenneth Falconer; Sang Velani; Agamemnon Zafeiropoulos

doi:10.1016/j.jmaa.2018.12.025

Marstrand's Theorem revisited: projecting sets of dimension zero

Victor Beresnevich, Kenneth Falconer, Sang Velani, Agamemnon Zafeiropoulos

Pure Mathematics

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

Abstract

We establish a refinement of Marstrand's projection theorem for Hausdorff dimension functions finer than the usual power functions, including an analogue of Marstrand's Theorem for logarithmic Hausdorff dimension.

Original language	English
Pages (from-to)	1820-1845
Number of pages	26
Journal	Journal of Mathematical Analysis and Applications
Volume	472
Issue number	2
Early online date	11 Dec 2018
DOIs	https://doi.org/10.1016/j.jmaa.2018.12.025
Publication status	Published - 15 Apr 2019

Keywords

Hausdorff measure/dimension
Potential theory
Orthogonal projections

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10.1016/j.jmaa.2018.12.025

Beresnevich-2018-Marstrand-Theorem-JMAA-AAM
© 2018, Elsevier Inc. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jmaa.2018.12.025
Accepted author manuscript, 463 KBLicence: CC BY-NC-ND

Cite this

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title = "Marstrand's Theorem revisited: projecting sets of dimension zero",

abstract = "We establish a refinement of Marstrand's projection theorem for Hausdorff dimension functions finer than the usual power functions, including an analogue of Marstrand's Theorem for logarithmic Hausdorff dimension.",

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author = "Victor Beresnevich and Kenneth Falconer and Sang Velani and Agamemnon Zafeiropoulos",

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AU - Falconer, Kenneth

AU - Velani, Sang

AU - Zafeiropoulos, Agamemnon

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AB - We establish a refinement of Marstrand's projection theorem for Hausdorff dimension functions finer than the usual power functions, including an analogue of Marstrand's Theorem for logarithmic Hausdorff dimension.

KW - Hausdorff measure/dimension

KW - Potential theory

KW - Orthogonal projections

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DO - 10.1016/j.jmaa.2018.12.025

M3 - Article

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SP - 1820

EP - 1845

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Marstrand's Theorem revisited: projecting sets of dimension zero

Abstract

Keywords

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