Theorems · Theorem · functional analysis

lp.norm_holderL_le

∀ {ι : Type u_1} {𝕜 : Type u_2} {E : ι → Type u_3} {F : ι → Type u_4} {G : ι → Type u_5} [inst : RCLike 𝕜]
  [inst_1 : (i : ι) → NormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)]
  [inst_3 : (i : ι) → NormedAddCommGroup (F i)] [inst_4 : (i : ι) → NormedSpace 𝕜 (F i)]
  [inst_5 : (i : ι) → NormedAddCommGroup (G i)] [inst_6 : (i : ι) → NormedSpace 𝕜 (G i)] {p q : ENNReal} (r : ENNReal)
  [hpqr : p.HolderTriple q r] [inst_7 : Fact (1 ≤ p)] [inst_8 : Fact (1 ≤ q)] [inst_9 : Fact (1 ≤ r)]
  (B : (i : ι) → E i →L[𝕜] F i →L[𝕜] G i) {K : NNReal} (hBK : ∀ (i : ι), ‖B i‖ ≤ ↑K), ‖lp.holderL r B hBK‖ ≤ ↑K

Defined in

Mathlib.Analysis.Normed.Lp.lpHolder

Cited by

1 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceENNReal.HolderTripleFactFactFact