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The Classes N(X) and RPD(X) : Integral Representations,s introduced by Schoenberg and recently refined by Bretagnolle, Dacunha Castelle, and Krivine , and Kuelbs , we are going to present characterizations of the classes RPD(.) and .(.) when . is one of the spaces ℝ. or . (. = 1,2, … ; 0 < . ≤ ∞ ).
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,The Extension Problem for Lipschitz-Hölder Maps between , Spaces, In this chapter we treat the natural and interesting generalization of this result to . spaces. Starting with two σ-finite measure spaces (Ω, μ) and (.) and initial values for . and . in , the problem is to determine those values of α for which the pair (.(μ), .(.)) has the extension property
Kandikere R. Sridhar,Namera C. Karunbedded in a given Banach space. First, we consider the question of which metric spaces (.) can be isometrically embedded in a Hilbert space ., that is, under what metric conditions does there exist a map ϕ: . → . such that $$|phi(s)-phi(t)|=
ho(s,t)$$ (1.1) for all points . and . in .? Secondly, we
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Anita Kumari,Jyoti Upadhyay,Rohit Joshire natural relatives of inequality (4.15) and the now standard inequalities of Clarkson. These inequalities are crucial to the problem of extending Lipschitz-Hölder maps of order a between . spaces (see §19). In addition they are of considerable intrinsic interest, a point we here emphasize by apply
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