CarlesonOnTheRealLine.lean`

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Annotation provenance. This overlay contains 10 curated AI-written annotations and 981 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

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Project sources: Pinned project documentation, Pinned Carleson blueprint

2 declarations, 0 contain sorry, 0 declared as axioms

Imports (2)

Imported by 2 files

lemma general_carlesonOperator_on_the_reals_hasStrongType Version of Lemma 11.1.5 for general exponents line 16 source
Source comment
Version of Lemma 11.1.5 for general exponents

depends on sorry what this means
Statement uses: NNReal, Membership.mem, Set, Set.Ioo, OfNat.ofNat, Nat, MeasureTheory.HasStrongType, Complex, ENNReal, Real, carlesonOperator, HPow.hPow, K, MeasureTheory.MeasureSpace.volume, C_carleson_hasStrongType
Proof uses: Countable, FunctionDistances.Θ, two_sided_metric_carleson_hasStrongType, Mathlib.Meta.NormNum.isNat_le_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.true, Hilbert_strong_2_2
72 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
```
lemma general_carlesonOperator_on_the_reals_hasStrongType {q : ℝ≥0} (hq : q ∈ Set.Ioo 1 2) :
    HasStrongType (carlesonOperator K) q q volume volume (C_carleson_hasStrongType 4 q) := by
…
```
Mentions: carlesonOperator, K, C_carleson_hasStrongType
lemma rcarleson' Replacement for Lemma 11.1.5 line 36 source
Source comment
Replacement for Lemma 11.1.5

depends on sorry what this means
Statement uses: NNReal, Membership.mem, Set, Set.Ioo, OfNat.ofNat, Nat, Real, Complex, MeasureTheory.MemLp, MeasureTheory.MeasureSpace.volume, LE.le, ENNReal, MeasureTheory.eLpNorm, carlesonOperatorReal, K, HMul.hMul, C_carleson_hasStrongType
Proof uses: le_trans, carlesonOperator, HPow.hPow, MeasureTheory.eLpNorm_mono_enorm, carlesonOperatorReal_le_carlesonOperator, And.right, MeasureTheory.AEStronglyMeasurable, general_carlesonOperator_on_the_reals_hasStrongType
85 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
```
lemma rcarleson' {q : ℝ≥0} (hq : q ∈ Set.Ioo 1 2) {f : ℝ → ℂ} (hf : MemLp f q) :
    eLpNorm (T f) q ≤ (C_carleson_hasStrongType 4 q) * eLpNorm f q := by
…
```
Mentions: T, C_carleson_hasStrongType