Best Constants in Kahane-Khintchine Inequalities in Orlicz Spaces
نویسندگان
چکیده
منابع مشابه
Best Constants in Kahane-Khintchine Inequalities in Orlicz Spaces
Several inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. For this the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the well-known estimates for subnormal random variables, see [9], the third one is a consequence of a certain Gaussian-Jensen’s majorization technique, see [6], and the f...
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for all z1; . . . ; zn 2 C and all n 1 . The constant p 2 is shown to be the best possible. The method of proof relies upon a combinatorial argument, Taylor expansion, and the central limit theorem. The result is additionally strengthened by showing that the underlying functions are Schur-concave. The proof of this fact uses a result on multinomial distribution of Rinott, and Schur’s propositio...
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Several maximal inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. The method relies upon Lévy’s inequality and the technique established in [14] which is obtained by Haagerup-Young-Stechkin’s best possible constants in the classical Khintchine inequalities. Moreover by using Donsker’s invariance principle it is shown that the numerical constant in the inequality dedu...
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We obtain new proofs with improved constants of the Khintchine-type inequality with matrix coefficients in two cases. The first case is the Pisier and Lust-Piquard noncommutative Khintchine inequality for p = 1 , where we obtain the sharp lower bound of 1 √ 2 in the complex Gaussian case and for the sequence of functions {en}n=1 . The second case is Junge’s recent Khintchine-type inequality for...
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We use gradient estimates for solutions of elliptic equations to obtain Korn’s inequality for fields with zero trace from Orlicz–Sobolev classes. As outlined for example in the monographs of Málek, Nečas, Rokyta, Růžička [MNRR], of Duvaut and Lions [DL] and of Zeidler [Ze], the well-posedness of many variational problems arising in fluid mechanics or in the mechanics of solids heavily depends o...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1993
ISSN: 0047-259X
DOI: 10.1006/jmva.1993.1033