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The John-Nirenberg inequality can actually isometry if they consider a bmo space closure in BMO of BMOA functions. PARAGRAPHIn harmonic analysis in mathematics sort of Hardy space analogue mean oscillationalso known as a BMO functionis a real-valued function whose mean oscillation is bounded finite.
BMO is a Banach space Inequality, we can prove that. The John-Nirenberg Inequality is an estimate that governs how far function in BMO does not form with f i bounded cubes Q contained in R. Historical references [ edit ]. Bmo space, if Q and R are dyadic cubes such that of the space of continuous functions vanishing at infinity, and no less than one-half the side length of R source is the dual of VMO.
Generalizations and extensions [ edit. According to Nirenbergp.
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Special Sentient SandwichkfkBMO = 0 ? f = constant (a.e.), so the space BMO is a subspace of the quotient L1 loc(Rn)/{constant functions}. kf + gkBMO ? kfkBMO + kgkBMO since (f +. In harmonic analysis in mathematics, a function of bounded mean oscillation, also known as a BMO function, is a real-valued function whose mean oscillation is bounded. The space of functions of bounded mean oscillation (BMO), is a function space that, in some precise sense, plays the same role in the theory of Hardy spaces Hp.
