On operators from to or to
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Hans Triebel (1994)
Studia Mathematica
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Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .
Reynaldo Rojas-Hernández (2015)
Commentationes Mathematicae Universitatis Carolinae
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We show that any -product of at most -many -spaces has the -property. This result generalizes some known results about -spaces. On the other hand, we prove that every -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...
Shaban Khidr, Osama Abdelkader (2017)
Czechoslovak Mathematical Journal
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Let be a -convex intersection, , , in a complex manifold of complex dimension , , and let be a holomorphic vector bundle of rank over . In this paper, -estimates, , for solutions to the -equation with small loss of smoothness are obtained for -valued -forms on when . In addition, we solve the -equation with a support condition in -spaces. More precisely, we prove that for a -closed form in , , , with compact support and for with there...
Wei-Feng Xuan, Wei-Xue Shi (2017)
Commentationes Mathematicae Universitatis Carolinae
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We prove that if is a first countable space with property and with a -diagonal then the cardinality of is at most . We also show that if is a first countable, DCCC, normal space then the extent of is at most .
Fabien Durand (2011)
Journal of the European Mathematical Society
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The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let and be two multiplicatively independent Perron numbers. Then a sequence , where is a finite alphabet, is both -substitutive and -substitutive if and only if is ultimately...
Sandro Manfredini, Simona Settepanella (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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Let be the -th ordered configuration space of all distinct points in the Grassmannian of -dimensional subspaces of , whose sum is a subspace of dimension . We prove that is (when non empty) a complex submanifold of of dimension and its fundamental group is trivial if , and and equal to the braid group of the sphere if . Eventually we compute the fundamental group in the special case of hyperplane arrangements, i.e. .
Mei-Chu Chang, Jozsef Solymosi (2007)
Journal of the European Mathematical Society
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In this paper we prove the following theorems in incidence geometry. 1. There is such that for any , and , if there are many distinct lines between and for all , , then are collinear. If the number of the distinct lines is then the cross ratio of the four points is algebraic. 2. Given , there is such that for any noncollinear, and , if there are many distinct lines between and for all , , then for any , we have distinct lines between and . 3. Given...
B. Jasek
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CONTENTSPREFACE..........................................................................................................................................................................3INTRODUCTION............................................................................................................................................................. 41. Notation. 2. Subject of the paper.Chapter I. DECOMPOSITION OF Σ INTO , , , INESSENTIAL RESTRICTIONOF GENERALITY ...............................................................................................................................................................
Andreas M. Fröhlich, Lutz Weis (2006)
Bulletin de la Société Mathématique de France
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We characterise the boundedness of the calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if generates a bounded analytic semigroup on a UMD space, then the calculus of is bounded if and only if has a dilation to a bounded group on . This generalises a Hilbert space result of C.LeMerdy. If is an space we can choose another space in place of .
Jiří Matoušek, Martin Tancer, Uli Wagner (2011)
Journal of the European Mathematical Society
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Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all...