Results 151 to 160 of about 24,314 (174)
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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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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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Journal d'Analyse Mathématique, 2001
Let \(f\) denote an ACL sense-preserving open and discrete mapping defined in a domain of the complex plane (where ACL stands for absolutely continuous on lines). Then the complex dilatation \(\mu(z)=\overline \partial f(z)/ \partial f(z)\) with \(|\mu |
Ryazanov, V., Srebro, U., Yakubov, E.
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Let \(f\) denote an ACL sense-preserving open and discrete mapping defined in a domain of the complex plane (where ACL stands for absolutely continuous on lines). Then the complex dilatation \(\mu(z)=\overline \partial f(z)/ \partial f(z)\) with \(|\mu |
Ryazanov, V., Srebro, U., Yakubov, E.
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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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Weighted Weak-Type BMO-Regularity
Journal of Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mappings of BMO–bounded distortion
Mathematische Annalen, 2000In this paper the authors continue developing the theme of mappings of \(BMO\)-bounded distortion, refining and extending previous work, as well as obtaining new results. Let \(\Omega\) be an open subset of \(\mathbb{R}^n\). A function \(f:\Omega\rightarrow\mathbb{R}^n\) is said to have finite distortion if \(f\in W_{\text{loc}}^{1,\phi}(\Omega,\mathbb{
Astala, Kari +3 more
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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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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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Transactions of the American Mathematical Society, 1985
Summary: We consider subspaces of \(BMO(R^ n)\) generated by one singular integral transform. We show that the averages along \(x_ j\)-lines of the jth Riesz transform of \(g\in BMO\cap L^ 2(R^ n)\) or \(g\in L^{\infty}(R^ n)\) satisfy a certain strong regularity property. One consequence of this result is that such functions satisfy a uniform doubling
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Summary: We consider subspaces of \(BMO(R^ n)\) generated by one singular integral transform. We show that the averages along \(x_ j\)-lines of the jth Riesz transform of \(g\in BMO\cap L^ 2(R^ n)\) or \(g\in L^{\infty}(R^ n)\) satisfy a certain strong regularity property. One consequence of this result is that such functions satisfy a uniform doubling
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