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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Lisa Nilsson, Damián Pinasco, Ignacio M. Zalduendo (2015)
Czechoslovak Mathematical Journal
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Starting from Lagrange interpolation of the exponential function in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space . Given such a representable entire funtion , in order to study the approximation problem and the uniform convergence of these polynomials to on bounded sets of , we present a sufficient growth condition on...