Characterization of n-rectifiability in terms of Jones’ square function: part I

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Abstract

© 2015, Springer-Verlag Berlin Heidelberg. In this paper it is shown that if μ is a finite Radon measure in Rd which is n-rectifiable and 1≤p≤2, then (Formula Presented),where (Formula Presented),with the infimum taken over all the n-planes L⊂Rd. The (Formula Presented) coefficients are the same as the ones considered by David and Semmes in the setting of the so called uniform n-rectifiability. An analogous necessary condition for n-rectifiability in terms of other coefficients involving some variant of the Wasserstein distance W1 is also proved.
Original languageEnglish
Pages (from-to)3643-3665
JournalCalculus of Variations and Partial Differential Equations
Volume54
Issue number4
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

  • 28A75
  • 28A78
  • 42B20

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