On arithmetic sums of Ahlfors-regular sets
Orponen, T. (2022). On arithmetic sums of Ahlfors-regular sets. Geometric and Functional Analysis, 32(1), 81-134. https://doi.org/10.1007/s00039-021-00589-x
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Geometric and Functional AnalysisDate
2022Copyright
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Let A,B⊂RA,B⊂R be closed Ahlfors-regular sets with dimensions dimHA=:αdimHA=:α and dimHB=:βdimHB=: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=0dimHE=0.
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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.License
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