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a few comments
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fpvandoorn committed Feb 26, 2025
1 parent a1a092a commit f8d081b
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3 changes: 2 additions & 1 deletion Carleson/ToMathlib/HardyLittlewood.lean
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Expand Up @@ -71,7 +71,8 @@ variable {X E : Type*} {A : ℝ≥0} [MetricSpace X] [MeasurableSpace X]
{f : X → E} {x : X} {ι : Type*} {𝓑 : Set ι} {c : ι → X} {r : ι → ℝ}
-- feel free to assume `A ≥ 16` or similar

/-- Use the dominated convergence theorem [Folland, Lemma 3.16] -/
/-- Use the dominated convergence theorem
e.g. [Folland, Real Analysis. Modern Techniques and Their Applications, Lemma 3.16] -/
lemma continuous_average_ball (hf : LocallyIntegrable f μ) :
ContinuousOn (fun x : X × ℝ ↦ ⨍⁻ y in ball x.1 x.2, ‖f y‖ₑ ∂μ) (univ ×ˢ Ioi 0) := by
sorry
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2 changes: 2 additions & 0 deletions Carleson/ToMathlib/WeakType.lean
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Expand Up @@ -596,6 +596,8 @@ lemma HasWeakType.const_smul {𝕜 E' α α' : Type*} [NormedAddCommGroup E']
{p p' : ℝ≥0∞} {μ : Measure α} {ν : Measure α'} {c : ℝ≥0} (h : HasWeakType T p p' μ ν c)
[NormedRing 𝕜] [MulActionWithZero 𝕜 E'] [BoundedSMul 𝕜 E'] (k : 𝕜) :
HasWeakType (k • T) p p' μ ν (‖k‖₊ * c) := by
intro f hf
refine ⟨aestronglyMeasurable_const.smul (h f hf).1, ?_⟩
sorry

lemma HasWeakType.const_mul {E' α α' : Type*} [NormedRing E']
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2 changes: 1 addition & 1 deletion Carleson/TwoSidedCarleson/WeakCalderonZygmund.lean
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Expand Up @@ -60,7 +60,7 @@ theorem ball_covering {O : Set X} (hO : IsOpen O ∧ O ≠ univ) :
∀ x ∈ O, Cardinal.mk { i | x ∈ ball (c i) (3 * r i)} ≤ (2 ^ (6 * a) : ℕ) := by
sorry

/-! ### Remarks about Lemma 10.2.5
/-! ### Lemma 10.2.5
Lemma 10.2.5 has an annoying case distinction between the case `E_α ≠ X` (general case) and
`E_α = X` (finite case). It isn't easy to get rid of this case distinction.
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