Theorems · Theorem · functional analysis
SchwartzMap.norm_fourier_apply_le_toLp_one
∀ {V : Type u_3} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : FiniteDimensional ℝ V]
[inst_3 : MeasurableSpace V] [inst_4 : BorelSpace V] {F : Type u_4} [inst_5 : NormedAddCommGroup F]
[inst_6 : NormedSpace ℂ F] (f : SchwartzMap V F) (x : V),
‖(FourierTransform.fourier f) x‖ ≤ ‖f.toLp 1 MeasureTheory.volume‖- Cited by
- 2 results in Mathlib
- Foundations
- Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- AddSubgroupstatement · cited by 3,232
- FiniteDimensionalstatement and proof · cited by 1,854
- MeasureTheory.integralproof · cited by 1,779
Cited by2
Results whose statement or proof uses this declaration.
- SchwartzMap.norm_fourier_Lp_top_leq_toLp_oneproof · cited by 0
- SchwartzMap.norm_fourier_toBoundedContinuousFunction_le_toLp_oneproof · cited by 0