fpvandoorn/carleson
Source indexedlemma · leanprover/lean4:v4.32.0
MeasureTheory.AEStronglyMeasurable.adjointCarleson
Carleson.Operators · Carleson/Operators.lean:251 to 261
Mathematical statement
Exact Lean statement
@[fun_prop]
lemma AEStronglyMeasurable.adjointCarleson (hf : AEStronglyMeasurable f) :
AEStronglyMeasurable (adjointCarleson p f)Complete declaration
Lean source
Full Lean sourceLean 4
@[fun_prop]lemma AEStronglyMeasurable.adjointCarleson (hf : AEStronglyMeasurable f) : AEStronglyMeasurable (adjointCarleson p f) := by refine .integral_prod_right' (f := fun z ↦ conj (Ks (𝔰 p) z.2 z.1) * exp (Complex.I * (Q z.2 z.2 - Q z.2 z.1)) * f z.2) ?_ refine .mono_ac (.prod .rfl restrict_absolutelyContinuous) ?_ refine .mul (.mul ?_ ?_) hf.comp_snd · exact Complex.continuous_conj.comp_aestronglyMeasurable aestronglyMeasurable_Ks.prod_swap · refine Complex.continuous_exp.comp_aestronglyMeasurable (.const_mul (.sub ?_ ?_) _) · exact Measurable.aestronglyMeasurable (by fun_prop) · exact continuous_ofReal.comp_aestronglyMeasurable aestronglyMeasurable_Q₂.prod_swap