Theorems · Definition · functional analysis

ContinuousLinearMap.holderL

{α : Type u_1} →
  {𝕜 : Type u_2} →
    {E : Type u_3} →
      {F : Type u_4} →
        {G : Type u_5} →
          {m : MeasurableSpace α} →
            (μ : MeasureTheory.Measure α) →
              (p q r : ENNReal) →
                [hpqr : p.HolderTriple q r] →
                  [inst : NontriviallyNormedField 𝕜] →
                    [inst_1 : NormedAddCommGroup E] →
                      [inst_2 : NormedAddCommGroup F] →
                        [inst_3 : NormedAddCommGroup G] →
                          [inst_4 : NormedSpace 𝕜 E] →
                            [inst_5 : NormedSpace 𝕜 F] →
                              [inst_6 : NormedSpace 𝕜 G] →
                                (E →L[𝕜] F →L[𝕜] G) →
                                  [inst_7 : Fact (1 ≤ p)] →
                                    [inst_8 : Fact (1 ≤ q)] →
                                      [inst_9 : Fact (1 ≤ r)] →
                                        ↥(MeasureTheory.Lp E p μ) →L[𝕜]
                                          ↥(MeasureTheory.Lp F q μ) →L[𝕜] ↥(MeasureTheory.Lp G r μ)

MeasureTheory.Lp.holder as a continuous bilinear map.

Defined in

Mathlib.MeasureTheory.Function.Holder

Cited by

4 results in Mathlib

Foundations

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

Assumes

ENNReal.HolderTripleNontriviallyNormedFieldNormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpaceFactFactFact