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.
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Christian Samuel (2010)
Colloquium Mathematicae
Similarity:
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.
Marco Cicalese, Gian Paolo Leonardi (2013)
Journal of the European Mathematical Society
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We prove some results in the context of isoperimetric inequalities with quantitative terms. In the -dimensional case, our main contribution is a method for determining the optimal coefficients in the inequality , valid for each Borel set with positive and finite area, with and being, respectively, the and the of . In dimensions, besides proving existence and regularity properties of minimizers for a wide class of including the lower semicontinuous extension of , we...
Teerapat Srichan (2021)
Czechoslovak Mathematical Journal
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A natural number is said to be a -integer if , where and is not divisible by the th power of any prime. We study the distribution of such -integers in the Piatetski-Shapiro sequence with . As a corollary, we also obtain similar results for semi--free integers.
Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster (2019)
Czechoslovak Mathematical Journal
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We consider the equation where and () are positive continuous functions for all and . By a solution of the equation we mean any function , continuously differentiable everywhere in , which satisfies the equation for all . We show that under certain additional conditions on the functions and , the above equation has a unique solution , satisfying the inequality where the constant does not depend on the choice of .
Xin Wang, Ming-Sheng Liu (2021)
Czechoslovak Mathematical Journal
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The aim of this paper is to characterize the boundedness of two classes of integral operators from to in terms of the parameters , , , , and , , where is the Siegel upper half-space. The results in the presented paper generalize a corresponding result given in C. Liu, Y. Liu, P. Hu, L. Zhou (2019).
Moshe Marcus, Laurent Véron (2004)
Journal of the European Mathematical Society
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Let be a bounded domain of class in N and let be a compact subset of . Assume that and denote by the maximal solution of in which vanishes on . We obtain sharp upper and lower estimates for in terms of the Bessel capacity and prove that is -moderate. In addition we describe the precise asymptotic behavior of at points , which depends on the “density” of at , measured in terms of the capacity .
Václav Kryštof, Luděk Zajíček (2016)
Commentationes Mathematicae Universitatis Carolinae
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It is proved that real functions on which can be represented as the difference of two semiconvex functions with a general modulus (or of two lower -functions, or of two strongly paraconvex functions) coincide with semismooth functions on (i.e. those locally Lipschitz functions on for which and for each ). Further, for each modulus , we characterize the class of functions on which can be written as , where and are semiconvex with modulus (for some ) using a new...
Azam Babai, Zeinab Akhlaghi (2017)
Czechoslovak Mathematical Journal
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Let be a group and be the set of element orders of . Let and be the number of elements of order in . Let nse. Assume is a prime number and let be a group such that nse nse, where is the symmetric group of degree . In this paper we prove that , if divides the order of and does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.
Saylí Sigarreta, Saylé Sigarreta, Hugo Cruz-Suárez (2023)
Kybernetika
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For a fixed positive integer and a connected graph of order , whose minimum vertex degree is at least , a set is a total -dominating set, also known as a -tuple total dominating set, if every vertex has at least neighbors in . The minimum size of a total -dominating set for is called the total -domination number of , denoted by . The total -domination problem is to determine a minimum total -dominating set of . Since the exact problem is in general quite difficult...
Paolo Leonetti, Salvatore Tringali (2014)
Journal de Théorie des Nombres de Bordeaux
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Given an integer , let be pairwise coprime integers , a family of nonempty proper subsets of with “enough” elements, and a function . Does there exist at least one prime such that divides for some , but it does not divide ? We answer this question in the positive when the are prime powers and and are subjected to certain restrictions. We use the result to prove that, if and is a set of three or more primes that contains all prime divisors of any...
Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)
Mathematica Bohemica
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Let be a complex Hilbert space, a positive operator with closed range in and the sub-algebra of of all -self-adjoint operators. Assume onto itself is a linear continuous map. This paper shows that if preserves -unitary operators such that then defined by is a homomorphism or an anti-homomorphism and for all , where and is the Moore-Penrose inverse of . A similar result is also true if preserves -quasi-unitary operators in both directions such that there...
Rajendra K. Sharma, Gaurav Mittal (2022)
Mathematica Bohemica
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We give the characterization of the unit group of , where is a finite field with elements for prime and denotes the special linear group of matrices having determinant over the cyclic group .
Jhon J. Bravo, Jose L. Herrera (2020)
Archivum Mathematicum
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For an integer , let be the generalized Pell sequence which starts with ( terms) and each term afterwards is given by the linear recurrence . In this paper, we find all -generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence . ...
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 .
Jacek Dziubański, Jacek Zienkiewicz (2003)
Colloquium Mathematicae
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Let A = -Δ + V be a Schrödinger operator on , d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of if the maximal function belongs to , where is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space admits a special atomic decomposition.
Quanwu Mu, Minhui Zhu, Ping Li (2019)
Czechoslovak Mathematical Journal
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Let be an odd integer and be any given real number. We prove that if , , , , are nonzero real numbers, not all of the same sign, and is irrational, then for any real number with , the inequality has infinitely many solutions in prime variables , where for and for odd integer with . This improves a recent result in W. Ge, T. Wang (2018).