Isometric imbeddings of Euclidean spaces into finite dimensional $l_p$-spaces

AbstractA precise quantitative version of the following qualitative statement is proved: If a finite-dimensional normed space contains approximately Euclidean subspaces of all proportional dimensions, then every proportional dimensional quotient space has the same property.

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On Partial Isometries in Finite-Dimensional Euclidean Spaces

SIAM Journal on Applied Mathematics ◽

10.1137/0114040 ◽

1966 ◽

Vol 14 (3) ◽

pp. 453-467 ◽

Cited By ~ 8

Author(s):

Ivan Erdelyi

Keyword(s):

Euclidean Spaces ◽

Partial Isometries ◽

Finite Dimensional

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Littlewood-Paley theory on Gaussian spaces

Nagoya Mathematical Journal ◽

10.1017/s0027763000002750 ◽

1988 ◽

Vol 109 ◽

pp. 47-61 ◽

Cited By ~ 7

Author(s):

Jürgen Potthoff

Keyword(s):

Lebesgue Measure ◽

Measure Space ◽

Euclidean Spaces ◽

General Measure ◽

Finite Dimensional

In this article we prove a number of inequalities of Littlewood-Paley-Stein (LPS) type for functions on general Gaussian spaces (s. below).In finite dimensional Euclidean spaces (with Lebesgue measure) the power of such inequalities has been demonstrated in Stein’s book [12]. In his second book [13], Stein treats other spaces too: also the situation of a general measure space (X, μ). However the latter case is too general to allow for a rich class of inequalities (cf. Theorem 10 in [13]).

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A System of Differential Set-Valued Variational Inequalities in Finite Dimensional Spaces

Journal of Function Spaces ◽

10.1155/2014/918796 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Wei Li ◽

Xing Wang ◽

Nan-Jing Huang

Keyword(s):

Variational Inequalities ◽

Existence Theorem ◽

Weak Solutions ◽

Convergence Result ◽

Time Dependent ◽

Euclidean Spaces ◽

Finite Dimensional ◽

Differential Set

A system of differential set-valued variational inequalities is introduced and studied in finite dimensional Euclidean spaces. An existence theorem of weak solutions for the system of differential set-valued variational inequalities in the sense of Carathéodory is proved under some suitable conditions. Furthermore, a convergence result on Euler time-dependent procedure for solving the system of differential set-valued variational inequalities is also given.

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