Theorems · Theorem · functional analysis
TemperedDistribution.memSobolev_besselPotential_iff
∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
[inst_2 : InnerProductSpace ℝ E] [inst_3 : FiniteDimensional ℝ E] [inst_4 : MeasurableSpace E] [inst_5 : BorelSpace E]
[inst_6 : NormedSpace ℂ F] [inst_7 : CompleteSpace F] {s r : ℝ} {p : ENNReal} [hp : Fact (1 ≤ p)]
{f : TemperedDistribution E F},
TemperedDistribution.MemSobolev s p ((TemperedDistribution.besselPotential E F r) f) ↔
TemperedDistribution.MemSobolev (r + s) p f- Defined in
- Mathlib.Analysis.Distribution.Sobolev
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement and proof · cited by 9,879
- Set.Elemstatement · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
Cited by3
Results whose statement or proof uses this declaration.
- TemperedDistribution.MemSobolev.laplacianproof · cited by 0
- TemperedDistribution.MemSobolev.lineDerivOpproof · cited by 0
- TemperedDistribution.MemSobolev.monoproof · cited by 0