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Properties of BMO Functions whose Reciprocals are also BMO
Zeitschrift für Analysis und ihre Anwendungen, 1993The paper gives some properties of the space \(\text{BMO}_ *=\{w\in\text{BMO}: 1/\omega\in\text{BMO}\}\) such as Theorem 1. A real- valued function \(u\) is in \(\text{BMO }\Leftrightarrow\) there exists \(w\in \text{BMO}_ *\) such that \(u=w-1/w\) (a consequence of \(\text{Lip }\alpha\)-operatability on BMO); Theorem 3.
Johnson, R. L., Neugebauer, C. J.
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BMO estimates for the -Laplacian
Nonlinear Analysis: Theory, Methods & Applications, 2012The authors prove BMO estimates of the inhomogeneous \(p\)-Laplace system \[ -\text{div }(|\nabla u|^{p-2}\nabla u)=\text{div }f,\qquad p\in(1,\infty). \] It is shown that \(f\in\) BMO implies \(|\nabla u|^{p-2}\nabla u\in\) BMO, which is the limiting case of the nonlinear Calderón-Zygmund theory.
Diening, Lars +2 more
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Nonlinear Wavelet Approximation in BMO
Constructive Approximation, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ivanov, Kamen G., Petrushev, Pencho
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Acta Mathematica Scientia, 2000
Summary: A negative answer to a question raised by \textit{R. Durrett} [``Brownian motion and martingales in analysis'' (1984; Zbl 0554.60075)] about a BMO martingale is given.
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Summary: A negative answer to a question raised by \textit{R. Durrett} [``Brownian motion and martingales in analysis'' (1984; Zbl 0554.60075)] about a BMO martingale is given.
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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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Journal of the London Mathematical Society, 1994
In this paper we introduce the one-sided sharp functions defined by \[ f_ +^ \# (x) = \sup_{h > 0} {1 \over h} \int^{x + h}_ x \left( f(y) - {1 \over h} \int^{x + 2h}_{x + h} f \right)^ + dy \] and \[ f_ -^ \# (x) = \sup_{h > 0} {1 \over h} \int^ x_{x - h} \left( f(y) - {1 \over h} \int^{x - h}_{x-2h} f \right)^ + dy \] where \(z^ + = \max (z,0)\).
Martín-Reyes, F. J., de la Torre, A.
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In this paper we introduce the one-sided sharp functions defined by \[ f_ +^ \# (x) = \sup_{h > 0} {1 \over h} \int^{x + h}_ x \left( f(y) - {1 \over h} \int^{x + 2h}_{x + h} f \right)^ + dy \] and \[ f_ -^ \# (x) = \sup_{h > 0} {1 \over h} \int^ x_{x - h} \left( f(y) - {1 \over h} \int^{x - h}_{x-2h} f \right)^ + dy \] where \(z^ + = \max (z,0)\).
Martín-Reyes, F. J., de la Torre, A.
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Local to global results for spaces of $${{\mathrm{BMO}}}$$ BMO type
Mathematische Zeitschrift, 2015We study a class of spaces, $$JN_p$$ , related to $${{\mathrm{BMO}}}$$
Niko Marola, Olli Saari
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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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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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Mathematische Nachrichten, 1999
AbstractLet P be an elliptic differential operator of order p with real analytic coefficients on in open set Q ⊂ ℝn. Given a compact set K ⊂ Ω, we describe the closure in BMO(K) of the space of mentions of Pf = 0 on neighborhoods of K.
Korey, Michael, Tarkhanov, Nikolai
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AbstractLet P be an elliptic differential operator of order p with real analytic coefficients on in open set Q ⊂ ℝn. Given a compact set K ⊂ Ω, we describe the closure in BMO(K) of the space of mentions of Pf = 0 on neighborhoods of K.
Korey, Michael, Tarkhanov, Nikolai
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Inequalities for BMO on α-Trees
International Mathematics Research Notices, 2015We develop technical tools that enable the use of Bellman functions for BMO defined on $α$-trees, which are structures that generalize dyadic lattices. As applications, we prove the integral John--Nirenberg inequality and an inequality relating $L^1$- and $L^2$-oscillations for BMO on $α$-trees, with explicit constants. When the tree in question is the
Slavin, Leonid, Vasyunin, Vasily
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