1,721,310 research outputs found
Why Hölder's inequality should be called Rogers' inequality
Full text linkThis reviewer remembers Leopold Fejér (1880-1959) saying (in Hungarian) that ``the history of mathematics serves to prove that nobody discovered anything: there was always somebody who had known it before'' (quoted in English in the present paper). The author argues convincingly about who had priority to the inequalities of Hölder (Rogers), Cauchy (Lagrange), Jensen (Hölder) and others. Also equivalences and relations between different forms and different inequalities and several proofs are offered. The paper concludes with biographical sketches of Leonard James Rogers and Otto Ludwig Hölder.Godkänd; 1998; 20070112 (kani)</p
Indices and interpolation
No full textThe author gives a systematic exposition of several aspects of indices of functions (indices of submultiplicative and measurable functions), various indices of Orlicz functions and indices of rearrangement invariant spaces defined by Boyd and Zippin. He gives various instances from interpolation theory in which indices play an important role.Upprättat; 1985; 20090226 (evan)</p
Indices and interpolation [Elektronisk resurs]
No full textThe author gives a systematic exposition of several aspects of indices of functions (indices of submultiplicative and measurable functions), various indices of Orlicz functions and indices of rearrangement invariant spaces defined by Boyd and Zippin. He gives various instances from interpolation theory in which indices play an important role.</p
On Orlicz results in interpolation theory
No full textThe paper presents an interesting review of the work of W. Orlicz in interpolation theory, both for linear operators and for Lipschitz operators. The author provides new proofs for some of the theorems, based on developments in general interpolation theory. In addition, some open problems related to these results are discussed.Godkänd; 1991; Bibliografisk uppgift: Sider: 1-12; 20090302 (evan
On Orlicz results in interpolation theory [Elektronisk resurs]
No full textThe paper presents an interesting review of the work of W. Orlicz in interpolation theory, both for linear operators and for Lipschitz operators. The author provides new proofs for some of the theorems, based on developments in general interpolation theory. In addition, some open problems related to these results are discussed.</p
Type, cotype and convexity properties of quasi-Banach spaces
No full textResults on quasi-Banach spaces, their type and cotype together with the convexity and concavity of quasi-Banach lattices are collected. Several proofs are included. Then the Lebesgue , the Lorentz and the Marcinkiewicz spaces are the special examples. We review also several results of Kami\'nska and the author on convexity, concavity, type and cotype of general Lorentz spaces Godkänd; 2004; Bibliografisk uppgift: Varianttitel: Banach and function spaces; 20070116 (kani
Proceedings of the International Symposium on Banach and Function Spaces II (ISBFS 2006), Kyushu Institute of Technology, Kitakyushu, Japan, 14-17 September 2006
No full textGodkänd; 2008; 20081009 (evan
Positive bilinear operators in Calderón-Lozanovskii spaces
No full textA generalization of an abstract Hölder-Rogers inequality for positive bilinear operators is proved. Then it is used in the theory of interpolation of operators. An interpolation theorem for positive bilinear operators between Calderón-Lozanovskii spaces holds if and only if the parameter functions generating those spaces satisfy a generalized C-supermultiplicativity condition (2). In the case when all generating functions are the same this condition is exactly the same as the C-supermultiplicativity condition on the function.Validerad; 2003; 20070122 (evan
Type, cotype and convexity properties of quasi-Banach spaces [Elektronisk resurs]
No full textResults on quasi-Banach spaces, their type and cotype together with the convexity and concavity of quasi-Banach lattices are collected. Several proofs are included. Then the Lebesgue , the Lorentz and the Marcinkiewicz spaces are the special examples. We review also several results of Kami\'nska and the author on convexity, concavity, type and cotype of general Lorentz spaces </p
Proceedings of the International Symposium on Banach and Function Spaces II (ISBFS 2006), Kyushu Institute of Technology, Kitakyushu, Japan, 14-17 September 2006
No full textGodkänd; 2008; 20081009 (evan
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