fpvandoorn/carleson
Source indexedlemma · leanprover/lean4:v4.32.0
MeasureTheory.StronglyMeasurable.adjointCarleson
Carleson.Operators · Carleson/Operators.lean:240 to 249
Mathematical statement
Exact Lean statement
@[fun_prop]
lemma StronglyMeasurable.adjointCarleson (hf : StronglyMeasurable f) :
StronglyMeasurable (adjointCarleson p f)Complete declaration
Lean source
Full Lean sourceLean 4
@[fun_prop]lemma StronglyMeasurable.adjointCarleson (hf : StronglyMeasurable f) : StronglyMeasurable (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 .mul (.mul ?_ ?_) (by fun_prop) · exact Complex.continuous_conj.comp_stronglyMeasurable (stronglyMeasurable_Ks.prod_swap) · refine Complex.continuous_exp.comp_stronglyMeasurable (.const_mul (.sub ?_ ?_) _) · exact Measurable.stronglyMeasurable (by fun_prop) · exact continuous_ofReal.comp_stronglyMeasurable stronglyMeasurable_Q₂.prod_swap