FUNCTIONS OF BOUNDED MEAN OSCILLATION

By Der-Chen Chang, Cora Sadosky. 2006

703 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b4e3b7240c5147db66a8d42566b25a16a1652bef

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1. Dachun Yang
2. Wen Yuan
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5. Yiyu Liang
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7. Jun Liu
8. Long Huang

Citations in the corpus

• Compactness Characterizations of Commutators on Ball Banach Function Spaces (2021, background): “John, F., Nirenberg, L.: On functions of bounded mean oscillation.”
• Endpoint estimates for n-dimensional Hardy operators and their commutators (2011, methodology): “H( a )χkkp p = Z 2k−1<|x|≤2k 1 υn|x|n Z |y|<1 (y)dy p dx = 0, where the last equality we used that R B(0,1) a (y)dy = 0. 3. Endpointestimates for commutators of n-dimensional Hardy operators In [8], John and Nirenberg introduced the space BMO. Define BMO(Rn) = {f : kfk BMO(Rn) < ∞}, where kf”
• Harnack Inequalities: An Introduction (2007, background): “Then the so-called John-Nirenberg inequality from [20] gives p0 > 0 and c = c(d) > 0 with ∫ Br (y) e (p0/K)|w−wy,r | ≤ c(d)rd and thus (3.”
• Sharp results in the integral-form John-Nirenberg inequality (2007, background): “In this paper, we are dealing with the space BMO that first appeared in the classical paper [3].”
• Localized BMO and BLO Spaces on RD-Spaces and Applications to Schr\ (2009, background): “In Section 3.1, we introduce a localized BMO-type space BMOρ(X ) and establish its several equivalent characterizations, John-Nirenberg inequality and some other properties; while Section 3.2 is devoted to the study of a corresponding localized BLO-type space BLOρ(X ).”
• Classes of Hardy spaces associated with operators, duality theorem and applications (2008, unknown): “For the basic facts about the classical Hardy and BMO spaces on Euclidean spaces R, see, for examples, [8], [21], [22], [30], [32] and [34].”
• Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications (2012, methodology): “Thus, we only need to prove that there exist positive constants C and c, independent of f and B0, such that for any λ ∈ (0,∞), |{x ∈ B0 : |f(x)| > λ}| ≤ Ce|B0|, whose proof is standard and we omit the details (see, for example, [32]).”
• Free boundary regularity below the continuous threshold: 2-phase problems (2006, background): “Since qW is Ahlfors regular and log hi A VMOðdsÞ by the John-Nirenberg theorem (see [11]) we have 38 Kenig and Toro, Free boundary regularity below the continuous threshold”
• On strong solutions of the Beltrami equations (2010, background): “The BMO space was introduced by John and Nirenberg [42] and soon became one of the main concepts in harmonic analysis, complex analysis and partial differential equations.”
• John–Nirenberg lemmas for a doubling measure (2009, methodology): “Nirenberg defined another, larger class of functions in their paper [11].”
• Morrey-Campanato Spaces: an Overview (2013, background): “Nirenberg [56] (1961) and defined, for open sets Ω ⊆ R, by the seminorm”
• The predual and John-Nirenberg inequalities on generalized BMO martingale spaces (2014, background): “1 Introduction Basing mainly on the duality, John-Nirenberg inequality and something else, the space BMO (Bounded Mean Oscillation; see [6], [7] and [12]) played a remarkable role in classical analysis and probability.”
• On Function Spaces with Mixed Norms — A Survey (2019, background): “Then the space L~a ~p,q,s(R) is just the classical Campanato space L 1 p−1,q,s (Rn) introduced by Campanato in [17], which includes the classical space BMO(Rn), introduced by John and Nirenberg in [46], as a special case.”
• A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations (2010, unknown): “To control the last expression, we need to recall the well-known John–Nirenberg inequality for BMO functions (see [14] or [27]): for any p ∈ (0,∞), ∥∥B(·, t) − B̄(t)∥∥ L(BR) Cp ∥∥B(·, t)∥∥BMO|BR|1/p.”
• Duality of Hardy and BMO spaces associated with operators with heat kernel bounds on product domains (2005, background): “These spaces were studied extensively in [32], [22], [18], [19], [31] and many others.”
• Global weighted estimates for the gradient of solutions to nonlinear elliptic equations (2013, background): “We would like to refer to [15,23,24,14,28,30] and references therein, where the notions about Bounded Mean Oscillation and Reifenberg flatness are extensively discussed, respectively.”