Theorems · Theorem · harmonic analysis

VectorFourier.norm_fourierIntegral_le_integral_norm

∀ {𝕜 : Type u_1} [inst : CommRing 𝕜] {V : Type u_2} [inst_1 : AddCommGroup V] [inst_2 : Module 𝕜 V]
  [inst_3 : MeasurableSpace V] {W : Type u_3} [inst_4 : AddCommGroup W] [inst_5 : Module 𝕜 W] {E : Type u_4}
  [inst_6 : NormedAddCommGroup E] [inst_7 : NormedSpace ℂ E] (e : AddChar 𝕜 Circle) (μ : MeasureTheory.Measure V)
  (L : V →ₗ[𝕜] W →ₗ[𝕜] 𝕜) (f : V → E) (w : W), ‖VectorFourier.fourierIntegral e μ L f w‖ ≤ ∫ (v : V), ‖f v‖ ∂μ

The uniform norm of the Fourier integral of f is bounded by the L¹ norm of f.

Defined in

Mathlib.Analysis.Fourier.FourierTransform

Cited by

4 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleMeasurableSpaceAddCommGroupModuleNormedAddCommGroupNormedSpace