Theorems · Theorem · functional analysis

SchwartzMap.norm_toLp_le_seminorm

∀ (𝕜 : Type u_2) {E : Type u_5} (F : Type u_6) [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : MeasurableSpace E]
  [inst_5 : OpensMeasurableSpace E] [inst_6 : NormedField 𝕜] [inst_7 : NormedSpace 𝕜 F] [inst_8 : SMulCommClass ℝ 𝕜 F]
  [inst_9 : SecondCountableTopologyEither E F] (p : ENNReal)
  (μ : autoParam (MeasureTheory.Measure E) SchwartzMap.norm_toLp_le_seminorm._auto_1) [hμ : μ.HasTemperateGrowth],
  ∃ k C, 0 ≤ C ∧ ∀ (f : SchwartzMap E F), ‖f.toLp p μ‖ ≤ C * ((Finset.Iic (k, 0)).sup (schwartzSeminormFamily 𝕜 E F)) f

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

0 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceOpensMeasurableSpaceNormedFieldNormedSpaceSMulCommClassSecondCountableTopologyEitherMeasureTheory.Measure.HasTemperateGrowth