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A characterization of BMO in terms of endpoint bounds for commutators of singular integrals
Israel Journal of Mathematics, 2018We provide a characterization of BMO in terms of endpoint boundedness of commutators of singular integrals. In particular, in one dimension, we show that ∥b∥BMO ≃ B, where B is the best constant in the endpoint L log L modular estimate for the commutator
Natalia Accomazzo
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, 1997 Recall from Ch. 6 that a function u on T is in L p (T) if and only if its Hubert transform Hu is. By virtue of (2.8) in Ch. 6, we can define the Hubert transform even for u ∈ L1(T) as a formal Fourier series; in general, it will not belong to L1(T) but merely be a distribution; cf. Remark 2.1 in Ch. 6.
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John–Nirenberg Inequalities and Weight Invariant BMO Spaces
Journal of Geometric Analysis, 2017This work explores new deep connections between John–Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMO-type spaces.
Jarod Hart, R. Torres
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BMO estimates for the -Laplacian [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2012 Abstract We prove BMO estimates of the inhomogeneous p -Laplace system given by − div ( | ∇ u | p − 2 ∇ u ) = div f . We show that f ∈ BMO implies | ∇ u | p − 2 ∇ u ∈ BMO , which is the limiting case of the nonlinear Calderon–Zygmund theory.
Diening, Lars +2 more
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BMO Solvability and Absolute Continuity of Harmonic Measure
, 2016We show that for a uniformly elliptic divergence form operator L, defined in an open set $$\Omega $$Ω with Ahlfors–David regular boundary, BMO solvability implies scale-invariant quantitative absolute continuity (the weak-$$A_\infty $$A∞ property) of ...
S. Hofmann, Phi Le
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Variational inequalities for the commutators of rough operators with BMO functions
Science China Mathematics, 2017Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation (BMO) functions can be obtained from their weighted variational estimates, we ...
Yanping Chen +3 more
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Dirichlet problem for Schrödinger equation with the boundary value in the BMO space
Science China Mathematics, 2022Renjin Jiang, Bo Li
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An Efficient Estimation Model for Induction Motor Using BMO-RBFNN Technique
Process Integration and Optimization for Sustainability, 2021P. Rajesh, F. H. Shajin, N. Vijaya Anand
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Analysis, 1995
Let \(B\) denote the unit ball in \(\mathbb{C}^n\), \(n \geq 1\), and \(m\) the \(2n\)-dimensional Lebesgue measure on \(B\) normalized by \(m(B) = 1\), and \(\sigma\) is the normalized surface measure on its boundary \(\partial B\). The main result is: Theorem. Let \(f \in L^2 (\sigma)\) and \(F = P[f]\) denotes Poisson- Szegö integral.
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Let \(B\) denote the unit ball in \(\mathbb{C}^n\), \(n \geq 1\), and \(m\) the \(2n\)-dimensional Lebesgue measure on \(B\) normalized by \(m(B) = 1\), and \(\sigma\) is the normalized surface measure on its boundary \(\partial B\). The main result is: Theorem. Let \(f \in L^2 (\sigma)\) and \(F = P[f]\) denotes Poisson- Szegö integral.
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