On ultra-weak convergence in
Donald E. Myers (1976)
Annales Polonici Mathematici
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Donald E. Myers (1976)
Annales Polonici Mathematici
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Adam Osękowski (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let α ∈ [0,1] be a fixed parameter. We show that for any nonnegative submartingale X and any semimartingale Y which is α-subordinate to X, we have the sharp estimate . Here W is the weak- space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of α-subordinate Itô processes.
Giovanni Alberti, Stefano Bianchini, Gianluca Crippa (2014)
Journal of the European Mathematical Society
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We characterize the autonomous, divergence-free vector fields on the plane such that the Cauchy problem for the continuity equation admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential associated to . As a corollary we obtain uniqueness under the assumption that the curl of is a measure. This result can be extended to certain non-autonomous vector fields with...
Madjid Eshaghi Gordji, Ali Jabbari, Abasalt Bodaghi (2019)
Mathematica Bohemica
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The generalized notion of weak amenability, namely -weak amenability, where are continuous homomorphisms on a Banach algebra , was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the -weak amenability on the measure algebra , the group algebra and the Segal algebra , where is a locally compact group, are studied. As a typical example, the -weak amenability of a special semigroup algebra is shown as well.
Agnieszka Kałamajska (2001)
Colloquium Mathematicae
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We study the functional , where u=(u₁, ..., uₘ) and each is constant along some subspace of ℝⁿ. We show that if intersections of the ’s satisfy a certain condition then is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on to have the equivalence: is weakly continuous if and only if f is Λ-affine.
Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let be the subspace of consisting of all weak -points. It is not hard to see that is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that is a -pseudocompact space for all .
Adam Osękowski (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let be the Haar system on [0,1]. We show that for any vectors from a separable Hilbert space and any , k = 0,1,2,..., we have the sharp inequality , n = 0,1,2,..., where W([0,1]) is the weak- space introduced by Bennett, DeVore and Sharpley. The above estimate is generalized to the sharp weak-type bound , where X and Y stand for -valued martingales such that Y is differentially subordinate to X. An application to harmonic functions on Euclidean domains is presented.
Panneerselvam Prabakaran (2020)
Commentationes Mathematicae Universitatis Carolinae
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Let be a ring, a fixed non-negative integer, the class of all left -modules with weak injective dimension at most , and the class of all right -modules with weak flat dimension at most . Using left (right) -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that is right balanced on by , and investigate the global right -dimension of by right derived functors of .
S. Gabriyelyan, J. Kąkol, G. Plebanek (2016)
Studia Mathematica
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Following Banakh and Gabriyelyan (2016) we say that a Tychonoff space X is an Ascoli space if every compact subset of is evenly continuous; this notion is closely related to the classical Ascoli theorem. Every -space, hence any k-space, is Ascoli. Let X be a metrizable space. We prove that the space is Ascoli iff is a -space iff X is locally compact. Moreover, endowed with the weak topology is Ascoli iff X is countable and discrete. Using some basic concepts from probability...
Umamaheswaran Arunachalam, Saravanan Raja, Selvaraj Chelliah, Joseph Kennedy Annadevasahaya Mani (2022)
Czechoslovak Mathematical Journal
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We introduce and study the concepts of weak -injective and weak -flat modules in terms of super finitely presented modules whose projective dimension is at most , which generalize the -FP-injective and -flat modules. We show that the class of all weak -injective -modules is injectively resolving, whereas that of weak -flat right -modules is projectively resolving and the class of weak -injective (or weak -flat) modules together with its left (or right) orthogonal class forms...
Zofia Adamowicz, Konrad Zdanowski (2011)
Fundamenta Mathematicae
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We prove that for i ≥ 1, the arithmetic does not prove a variant of its own Herbrand consistency restricted to the terms of depth in , where ε is an arbitrarily small constant greater than zero. On the other hand, the provability holds for the set of terms of depths in .
Jiecheng Chen, Dashan Fan, Yiming Ying (2002)
Studia Mathematica
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We give some rather weak sufficient condition for boundedness of the Marcinkiewicz integral operator on the product spaces (1 < p < ∞), which improves and extends some known results.
P. Mohanty, S. Madan (2003)
Studia Mathematica
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We prove that if and has compact support then Λ is a weak summability kernel for 1 < p < ∞, where is the space of multipliers of .
Chao Zhang, Shulin Zhou, Bin Ge (2015)
Annales Polonici Mathematici
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Under some assumptions on the function p(x), we obtain global gradient estimates for weak solutions of the p(x)-Laplacian type equation in .
Gioconda Moscariello (1998)
Annales Polonici Mathematici
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We prove a regularity result for weak minima of integral functionals of the form where F(x,ξ) is a Carathéodory function which grows as with some p > 1.
Kristóf Szarvas, Ferenc Weisz (2016)
Czechoslovak Mathematical Journal
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The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces (in the case ), but (in the case when is log-Hölder continuous and ) on the variable Lebesgue spaces , too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type . In the present note we generalize Besicovitch’s covering theorem for the so-called -rectangles. We introduce a general maximal operator and with the help of generalized -functions, the strong-...
Cholmin Sin (2023)
Czechoslovak Mathematical Journal
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We show time regularity of weak solutions for unsteady motion equations of generalized Newtonian fluids described by -power law for , by using a higher integrability property and fractional difference method. Moreover, as its application we prove that every weak solution to the problem becomes a local in time strong solution and that it is unique.
Figen Takıl Mutlu, Adnan Tercan, Ramazan Yaşar (2023)
Mathematica Bohemica
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In this article, we study modules with the weak -extending property. We prove that if satisfies weak -extending, pseudo duo, properties and has finite uniform dimension then decomposes into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if satisfies the weak -extending, pseudo duo, properties and ascending (or descending) chain condition on essential submodules then for some semisimple submodule and Noetherian (or...
Ushangi Goginava (2008)
Studia Mathematica
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The main aim of this paper is to prove that the maximal operator is bounded from the Hardy space to weak- and is not bounded from to .