Some capacities and applications - the lemma on mixed derivatives revisited
J. Korevaar (1986)
Matematički Vesnik
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J. Korevaar (1986)
Matematički Vesnik
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Jan Vybiral
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We study several techniques which are well known in the case of Besov and Triebel-Lizorkin spaces and extend them to spaces with dominating mixed smoothness. We use the ideas of Triebel to prove three important decomposition theorems. We deal with so-called atomic, subatomic and wavelet decompositions. All these theorems have much in common. Roughly speaking, they say that a function f belongs to some function space (say ) if, and only if, it can be decomposed as , convergence in S’, with...
Bogdan Rzepecki (1975)
Annales Polonici Mathematici
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Philippe Eyssidieux, Carlos Simpson (2011)
Journal of the European Mathematical Society
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Let be a compact Kähler manifold, be a base point and be the monodromy representation of a -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at and a variation of mixed Hodge structures whose monodromy is the universal deformation of .
W. Mlak (1963)
Annales Polonici Mathematici
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Denny H. Leung, Wee-Kee Tang (2006)
Studia Mathematica
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We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space : (1) Every block subspace of X contains an -spreading model, (2) The Bourgain ℓ¹-index for any block subspace Y of X, (3) and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these...
Lev Markhasin (2015)
Acta Arithmetica
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Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with...
Guangbin Ren, Jihuai Shi (2004)
Studia Mathematica
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For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space of the polydisc onto the mixed norm space of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.
Ewa Zadrzyńska
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CONTENTS1. Introduction....................................................................................................................................................52. Notations and preliminaries .........................................................................................................................11 2.1. Function spaces and spaces of distributions............................................................................................11 2.2. Perturbations...
J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2017)
Applications of Mathematics
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The authors provide a correction to “Some mean convergence and complete convergence theorems for sequences of -linearly negative quadrant dependent random variables”.
I. Assani (2005)
Colloquium Mathematicae
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We answer a question of H. Furstenberg on the pointwise convergence of the averages , where U and R are positive operators. We also study the pointwise convergence of the averages when T and S are measure preserving transformations.
Andrei K. Lerner, Kabe Moen (2013)
Studia Mathematica
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We establish several mixed bounds for Calderón-Zygmund operators that only involve one supremum. We address both cases when the part of the constant is measured using the exponential-logarithmic definition and using the Fujii-Wilson definition. In particular, we answer a question of the first author and provide an answer, up to a logarithmic factor, to a conjecture of Hytönen and Lacey. Moreover, we give an example to show that our bounds with the logarithmic factors can be arbitrarily...
Wiesław Królikowski
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We study several techniques which are well known in the case of Besov and Triebel-Lizorkin spaces and extend them to spaces with dominating mixed smoothness. We use the ideas of Triebel to prove three important decomposition theorems. We deal with so-called atomic, subatomic and wavelet decompositions. All these theorems have much in common. Roughly speaking, they say that a function f belongs to some function space (say ) if, and only if, it can be decomposed as , convergence in S’, with...
L. D. Ivanović, B. S. Jovanović, E. E. Süli (1984)
Matematički Vesnik
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Zhiting Xu (2010)
Annales Polonici Mathematici
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Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ , ⎨ ⎩ under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with mixed nonlinearities, and include some known oscillation results in the literature
Denka Kutzarova, Denny H. Leung, Antonis Manoussakis, Wee-Kee Tang (2008)
Studia Mathematica
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We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis is said to be subsequentially minimal if for every normalized block basis of , there is a further block basis of such that is equivalent to a subsequence of . Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain’s ℓ¹-index are established. It is also shown that a large class of...
Péter Kórus (2018)
Czechoslovak Mathematical Journal
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We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the -convergence of double Fourier series. We also give necessary and sufficient conditions for the -convergence under appropriate assumptions.
Larry Kitchens, Charles Swartz (1974)
Colloquium Mathematicae
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