OAI/Analysis/RieszRectifiability/Kernel/CappedRieszKernel.lean

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12 declarations, 0 contain sorry, 0 declared as axioms

Capped Riesz kernels

Capping the radial singularity gives a continuous bounded vector kernel agreeing with the Riesz kernel away from the cap. The scalar difference from hard truncation is controlled by a symmetric weight supported on close pairs.

  1. def OAI.RieszRectifiability.cappedRieszKernel line 20
  2. theorem OAI.RieszRectifiability.cappedRieszKernel_continuous line 24
  3. theorem OAI.RieszRectifiability.cappedRieszKernel_norm_bound line 30
  4. theorem OAI.RieszRectifiability.cappedRieszKernel_eq_kernel line 36
  5. def OAI.RieszRectifiability.scalarCappedRieszKernel line 43
  6. theorem OAI.RieszRectifiability.scalarCappedRieszKernel_continuous line 46
  7. theorem OAI.RieszRectifiability.scalarCappedRieszKernel_bound line 50
  8. def OAI.RieszRectifiability.closedNearCapWeight line 57
  9. theorem OAI.RieszRectifiability.closedNearCapWeight_measurable line 60
  10. theorem OAI.RieszRectifiability.closedNearCapWeight_nonneg line 64
  11. theorem OAI.RieszRectifiability.closedNearCapWeight_symm line 68
  12. theorem OAI.RieszRectifiability.scalarCappedRieszKernel_hard_error line 73