Results 191 to 200 of about 8,308 (225)
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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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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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On a BMO-Property for Subharmonic Functions
Journal of Fourier Analysis and Applications, 2002A compact set \(K\subset \mathbb{R}^2\) is called (Ahlfors) \(d\)-regular, if there exists \(a>0\) such that for any \(x\in K\) and ...
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Transactions of the American Mathematical Society, 1985
This paper concerns certain generalizations of BMO, the space of functions of bounded mean oscillation. Let \(\rho\) be a positive nondecreasing function on (0,\(\infty)\) with \(\rho (0+)=0\). A locally integrable function on \({\mathbb{R}}^ m\) is said to belong to BMO(\(\rho)\) if its mean oscillation over any cube Q is O(\(\rho\) (\(\ell (Q ...
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This paper concerns certain generalizations of BMO, the space of functions of bounded mean oscillation. Let \(\rho\) be a positive nondecreasing function on (0,\(\infty)\) with \(\rho (0+)=0\). A locally integrable function on \({\mathbb{R}}^ m\) is said to belong to BMO(\(\rho)\) if its mean oscillation over any cube Q is O(\(\rho\) (\(\ell (Q ...
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Two Characterizations of Central BMO Space via the Commutators of Hardy Operators
Forum Mathematicum, 2021Shaoguang Shi, Zunwei Fu, Shanzhen Lu
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