Theorems · Theorem · functional analysis

ContinuousLinearMap.memLp_of_bilin

∀ {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 : ENNReal} (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 : α → E} {g : α → F},
  MeasureTheory.MemLp f p μ → MeasureTheory.MemLp g q μ → MeasureTheory.MemLp (fun x => (B (f x)) (g x)) r μ

Defined in

Mathlib.MeasureTheory.Function.Holder

Cited by

3 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ENNReal.HolderTripleNontriviallyNormedFieldNormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpace