The John-Nirenberg Inequality and a Sobolev Inequality in General Domains
Journal of Mathematical Analysis and Applications, 1993 The classical John-Nirenberg lemma [\textit{F. John} and \textit{L. Nirenberg}, Commun. Pure Appl. Math. 14, 415-426 (1961; Zbl 0102.043)] states that if the mean oscillation of a function \(u\) in a cube \(D\) is uniformly bounded in each subcube, parallel to \(D\), then the oscillation of \(u\) is exponentially integrable in \(D\); more precisely, \[
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Good-λ Inequalities, Rearrangements, and the John-Nirenberg Theorem
Journal of Mathematical Analysis and Applications, 1993 The goal of this work is to prove an integral inequality of the form \[ {1 \over | Q_ 0 |} \int_{Q_ 0} \left | f(x)-{1 \over | Q_ 0 |} \int_{Q_ 0} f\right |^ pdx \leq C{1 \over | Q_ 0 |} \int_{Q_ 0} \left | f(x)-{1 \over | Q_ 0 |} \int_{Q_ 0} f \right | dx, \] for \(Q_ 0\) a cube in \(\mathbb{R}^ n\), with a constant \(C\) that does not depend on the ...
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The Hardy–Morrey & Hardy–John–Nirenberg inequalities involving distance to the boundary
Journal of Differential Equations, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Filippas, Stathis, Psaradakis, Georgios
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John–Nirenberg Inequalities for Noncommutative Column BMO and Lipschitz Martingales
Communications in Mathematical PhysicsIn this paper, we continue the study of John-Nirenberg theorems for BMO/Lipschitz spaces in the noncommutative martingale setting. As conjectured from the classical case, a desired noncommutative ``stopping time" argument was discovered to obtain the distribution function inequality form of John-Nirenberg theorem.
Guixiang Hong, Congbian Ma, Yu Wang
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Quantitative John--Nirenberg inequality for stochastic processes of bounded mean oscillation
, 2022 Stroock and Varadhan in 1997 and Geiss in 2005 independently introduced stochastic processes with bounded mean oscillation (BMO) and established their exponential integrability with some unspecified exponential constant. This result is an analogue of the John--Nirenberg inequality for functions of bounded mean oscillation. In this work, we quantify the
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Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation. [PDF]
Ann PDE, 2021 Colombo M, Haffter S.
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Self-Improving Properties of John–Nirenberg and Poincaré Inequalities on Spaces of Homogeneous Type
Journal of Functional Analysis, 1998 The authors consider inequalities of the form \[ \underset{\mu(B)}\bot \int_B| f-f_B| d\mu\leq ca(B)\quad\text{and} \quad \underset{\mu(B)}\bot \int_B | f-f_B| d\mu\leq cb(B,f). \] In either case \(\mu\) is a measure and \(\mu(B)\) denotes the \(\mu\)-measure of \(B\).
Franchi, Bruno +2 more
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A sharp symmetric integral form of the John–Nirenberg inequality
Proceedings of the American Mathematical SocietyWe find sharp constants in the symmetric integral form of the John–Nirenberg inequality. The result is based upon the computation of a new interesting Bellman function.
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Program Abstracts from The GSA 2021 Annual Scientific Meeting, "Disruption to Transformation: Aging in the "New Normal"". [PDF]
Innov Aging, 2021 europepmc +1 more source