OAI/Analysis/RieszRectifiability/Rigidity/FractionalGradientDomination.lean

GitHub source file

3 declarations, 0 contain sorry, 0 declared as axioms

An integrable dominator for fractional gradients

Schwartz derivative seminorms control the near and far parts separately, with inverse-distance powers p and p + 2. In dimension p + 1 their sum is integrable and uniformly bounds the dilated gradient kernel for dilation parameters between one half and two.

  1. def OAI.RieszRectifiability.fractionalGradientDominator line 23
  2. theorem OAI.RieszRectifiability.fractionalGradientDominator_integrable line 32
  3. theorem OAI.RieszRectifiability.dilatedFractionalGradientKernel_le_dominator line 42