Theorems · Theorem · functional analysis

ContinuousLinearMap.norm_holder_apply_apply_le

∀ {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] (B : E →L[𝕜] F →L[𝕜] G)
  (f : ↥(MeasureTheory.Lp E p μ)) (g : ↥(MeasureTheory.Lp F q μ)),
  ‖ContinuousLinearMap.holder r B f g‖ ≤ ‖B‖ * ‖f‖ * ‖g‖

Defined in

Mathlib.MeasureTheory.Function.Holder

Cited by

1 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ENNReal.HolderTripleNontriviallyNormedFieldNormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpace