Some Tauberian theorems on summability methods of integrals
B. P. Mishra, D. Singh (1976)
Matematički Vesnik
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B. P. Mishra, D. Singh (1976)
Matematički Vesnik
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L. Jeśmanowicz (1962)
Annales Polonici Mathematici
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B. Martić (1964)
Matematički Vesnik
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R. K. Jain, A. Ganguly (1978)
Matematički Vesnik
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Ferenc Weisz (2009)
Studia Mathematica
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It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space to . This implies the almost everywhere convergence of the Fejér means in a cone for all , which is larger than .
István Blahota, Lars-Erik Persson, Giorgi Tephnadze (2015)
Czechoslovak Mathematical Journal
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We prove and discuss some new -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of...
P. L. Sharma, R. K. Jain (1970)
Matematički Vesnik
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Ferenc Móricz (2004)
Colloquium Mathematicae
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Schmidt’s Tauberian theorem says that if a sequence (xk) of real numbers is slowly decreasing and , then . The notion of slow decrease includes Hardy’s two-sided as well as Landau’s one-sided Tauberian conditions as special cases. We show that ordinary summability (C,1) can be replaced by the weaker assumption of statistical summability (C,1) in Schmidt’s theorem. Two recent theorems of Fridy and Khan are also corollaries of our Theorems 1 and 2. In the Appendix, we present a new proof...
V. Swaminathan (1979)
Matematički Vesnik
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Boumediene Abdellaoui, Ireneo Peral (2006)
Journal of the European Mathematical Society
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The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes in , on , . This problem is a particular case of problem (2). Notice that is optimal as coefficient and exponent on the right hand side.
B. Jasek
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CONTENTSPREFACE..........................................................................................................................................................................3INTRODUCTION............................................................................................................................................................. 41. Notation. 2. Subject of the paper.Chapter I. DECOMPOSITION OF Σ INTO , , , INESSENTIAL RESTRICTIONOF GENERALITY ...............................................................................................................................................................
Francesca Angrisani, Giacomo Ascione (2018)
Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche
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Inspired by a result from Leibov, we find that the supremum defining the norm in is actually attained by a specific sub-interval of for
Tamás Erdélyi (2003)
Studia Mathematica
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Denote by spanf₁,f₂,... the collection of all finite linear combinations of the functions f₁,f₂,... over ℝ. The principal result of the paper is the following. Theorem (Full Clarkson-Erdős-Schwartz Theorem). Suppose is a sequence of distinct positive numbers. Then is dense in C[0,1] if and only if . Moreover, if , then every function from the C[0,1] closure of can be represented as an analytic function on z ∈ ℂ ∖ (-∞, 0]: |z| < 1 restricted to (0,1). This result improves an...
Sergey V. Astashkin, Lech Maligranda (2014)
Banach Center Publications
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Geometric structure of Cesàro function spaces , where I = [0,1] and [0,∞), is investigated. Among other matters we present a description of their dual spaces, characterize the sets of all q ∈ [1,∞] such that contains isomorphic and complemented copies of -spaces, show that Cesàro function spaces fail the fixed point property, give a description of subspaces generated by Rademacher functions in spaces .
Hartmut von Trotha
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CONTENTSIntroduction................................................................................................................................... 5 Notations.......................................................................................................................... 5§ 1. Preliminaries........................................................................................................................ 6 1. Right invertible operators.....................................................................................................
W. Szczotka (2006)
Applicationes Mathematicae
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For each n ≥ 1, let and be mutually independent sequences of nonnegative random variables and let each of them consist of mutually independent and identically distributed random variables with means v̅ₙ and u̅̅ₙ, respectively. Let , , t ≥ 0, and . The main result gives conditions under which the weak convergence , where X is a Lévy process, implies and , where and are mutually independent Lévy processes and .
A. R. Olfati (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let be a zero-dimensional space and be the set of all continuous real valued functions on with countable image. In this article we denote by (resp., the set of all functions in with compact (resp., pseudocompact) support. First, we observe that (resp., ), where is the Banaschewski compactification of and is the -compactification of . This implies that for an -compact space , the intersection of all free maximal ideals in is equal to , i.e., . By applying...
Bjorn Gabriel Walther (2002)
Colloquium Mathematicae
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We consider the maximal function where and 0 < a < 1. We prove the global estimate , s > a/4, with C independent of f. This is known to be almost sharp with respect to the Sobolev regularity s.
Biagio Ricceri (2003)
Colloquium Mathematicae
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We deal with the problem ⎧ -Δu = f(x,u) + λg(x,u), in Ω, ⎨ () ⎩ where Ω ⊂ ℝⁿ is a bounded domain, λ ∈ ℝ, and f,g: Ω×ℝ → ℝ are two Carathéodory functions with f(x,0) = g(x,0) = 0. Under suitable assumptions, we prove that there exists λ* > 0 such that, for each λ ∈ (0,λ*), problem () admits a non-zero, non-negative strong solution such that for all p ≥ 2. Moreover, the function is negative and decreasing in ]0,λ*[, where is the energy functional related to (). ...
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...
Lamberto Cesari (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In the present paper the author discusses certain multiple integrals of the calculus of variations satisfying convexity conditions, and no growth property, and the corresponding Serrin integrals , to which the existence theorems in [3,4,5] do not apply. However, in the present paper, the integrals and are reduced to simpler form and to which the existence theorems above apply. Thus, we derive that , , we obtain the existence of the absolute minimum for the Serrin forms ...