Theorems · Definition · functional analysis

SchwartzMap.toLpCLM

(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] →
                [OpensMeasurableSpace E] →
                  [inst_6 : NormedField 𝕜] →
                    [inst_7 : NormedSpace 𝕜 F] →
                      [inst_8 : SMulCommClass ℝ 𝕜 F] →
                        [SecondCountableTopologyEither E F] →
                          (p : ENNReal) →
                            [inst_10 : Fact (1 ≤ p)] →
                              (μ : autoParam (MeasureTheory.Measure E) SchwartzMap.toLpCLM._auto_1) →
                                [hμ : μ.HasTemperateGrowth] → SchwartzMap E F →L[𝕜] ↥(MeasureTheory.Lp F p μ)

Continuous linear map from Schwartz functions to L^p.

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

7 results in Mathlib

Foundations

Depth 235 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceOpensMeasurableSpaceNormedFieldNormedSpaceSMulCommClassSecondCountableTopologyEitherFactMeasureTheory.Measure.HasTemperateGrowth