Theorem 10.0.1 #
theorem two_sided_metric_carleson {X : Type u_1} {a : ℕ} [MetricSpace X] [MeasureTheory.DoublingMeasure X ↑(defaultA a)] {q q' : NNReal} {F G : Set X} {K : X → X → ℂ} [IsTwoSidedKernel a K] [CompatibleFunctions ℝ X (defaultA a)] [IsCancellative X (defaultτ a)] (ha : 4 ≤ a) (hq : q ∈ Set.Ioc 1 2) (hqq' : q.HolderConjugate q') (hF : MeasurableSet F) (hG : MeasurableSet G) (hT :
∀ r > 0, MeasureTheory.HasBoundedStrongType (czOperator K r) 2 2 MeasureTheory.volume MeasureTheory.volume ↑(C_Ts a)) {f : X → ℂ} (hmf : Measurable f) (hf : ∀ (x : X), ‖f x‖ ≤ F.indicator 1 x) :
∫⁻ (x : X) in G, carlesonOperator K f x ≤ ↑(C10_0_1 a q) * MeasureTheory.volume G ^ (↑q')⁻¹ * MeasureTheory.volume F ^ (↑q)⁻¹