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Update CarlesonOperatorReal.lean
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pitmonticone committed Jul 25, 2024
1 parent 42b0222 commit d948d00
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions Carleson/Classical/CarlesonOperatorReal.lean
Original file line number Diff line number Diff line change
Expand Up @@ -49,7 +49,7 @@ lemma sup_eq_sup_dense_of_continuous {f : ℝ → ENNReal} {S : Set ℝ} (D : Se

lemma helper {n : ℤ} {f : ℝ → ℂ} (hf : Measurable f) :
Measurable (Function.uncurry fun x y ↦ f y * K x y * (Complex.I * n * y).exp) :=
Measurable.mul (Measurable.mul (hf.comp measurable_snd) Hilbert_kernel_measurable)
((hf.comp measurable_snd).mul Hilbert_kernel_measurable).mul
(measurable_const.mul (Complex.measurable_ofReal.comp measurable_snd)).cexp

local notation "T" => CarlesonOperatorReal K
Expand Down Expand Up @@ -209,7 +209,7 @@ lemma CarlesonOperatorReal_measurable {f : ℝ → ℂ} (f_measurable : Measurab
rw [← stronglyMeasurable_iff_measurable]
apply MeasureTheory.StronglyMeasurable.integral_prod_right
rw [stronglyMeasurable_iff_measurable, Fdef]
exact Measurable.indicator (helper f_measurable) (measurable_dist measurableSet_Ioo)
exact (helper f_measurable).indicator (measurable_dist measurableSet_Ioo)

lemma CarlesonOperatorReal_mul {f : ℝ → ℂ} {x : ℝ} {a : ℝ} (ha : 0 < a) : T f x = a.toNNReal * T (fun x ↦ 1 / a * f x) x := by
rw [CarlesonOperatorReal, CarlesonOperatorReal, ENNReal.mul_iSup]
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