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On arithmetic sums of Ahlfors-regular sets

Abstract
Let A,B⊂RA,B⊂R be closed Ahlfors-regular sets with dimensions dimHA=:αdimH⁡A=:α and dimHB=:βdimH⁡B=:β. I prove that dimH[A+θB]≥α+β⋅1−α2−αdimH⁡[A+θB]≥α+β⋅1−α2−α for all θ∈R∖Eθ∈R∖E, where dimHE=0dimH⁡E=0.
Main Author
Orponen, Tuomas
Format
Articles Research article
Published
2022
Series
Geometric and Functional Analysis
Subjects
Ahlfors-regular sets
sum-product problem
Hausdorff dimension
aritmetiikka
mittateoria
kombinatoriikka
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/103881631
Publisher
Birkhäuser
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202201181174Use this for linking
Review status
Peer reviewed
ISSN
1016-443X
DOI
https://doi.org/10.1007/s00039-021-00589-x
Language
English
Published in
Geometric and Functional Analysis
Citation
License
CC BY 4.0Open Access
Additional information about funding
T.O. is supported by the Academy of Finland via the projects Quantitative rectifiability in Euclidean and non-Euclidean spaces and Incidences on Fractals, grant Nos. 309365, 314172, 321896. T.O. is also supported by the University of Helsinki via the project Quantitative rectifiability of sets and measures in Euclidean spaces and Heisenberg groups, project No. 7516125.
Copyright© 2022 the Authors

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