A pair of linear functional inequalities and a characterization of Lp-norm

An interesting result in convex analysis, established by J.-P. Crouzeix in 1977, states that a real-valued function defined on a linear space is convex if and only if each function obtained from it by adding a linear functional is quasiconvex. The aim of this paper is to extend this result for vector-valued functions taking values in a partially ordered linear space.

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A characterization of the sine function by functional inequalities

Mathematical Inequalities & Applications ◽

10.7153/mia-14-02 ◽

2011 ◽

pp. 13-33

Author(s):

Iwona Tyrala

Keyword(s):

Functional Inequalities ◽

Sine Function

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Maximal ideals in some F-algebras of holomorphic functions

Filomat ◽

10.2298/fil1501001m ◽

2015 ◽

Vol 29 (1) ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Romeo Mestrovic

Keyword(s):

Linear Functional ◽

Holomorphic Functions ◽

Complete Characterization ◽

Open Unit ◽

Continuous Linear ◽

Linear Functionals ◽

Continuous Linear Functional ◽

Maximal Ideals ◽

Algebras Of Holomorphic Functions

For 1 < p < ?, the Privalov class Np consists of all holomorphic functions f on the open unit disk D of the complex plane C such that sup 0?r<1?2?0 (log+ |f(rei?)j|p d?/2? < + ? M. Stoll [16] showed that the space Np with the topology given by the metric dp defined as dp(f,g) = (?2?0 (log(1 + |f*(ei?) - g*(ei?)|))p d?/2?)1/p, f,g ? Np; becomes an F-algebra. Since the map f ? dp(f,0) (f ? Np) is not a norm, Np is not a Banach algebra. Here we investigate the structure of maximal ideals of the algebras Np (1 < p < ?). We also give a complete characterization of multiplicative linear functionals on the spaces Np. As an application, we show that there exists a maximal ideal of Np which is not the kernel of a multiplicative continuous linear functional on Np.

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General form of linear continuous functional and criterion of the best approximant in spaces with mixed integral metric

Researches in Mathematics ◽

10.15421/241411 ◽

2014 ◽

Vol 22 ◽

pp. 91

Author(s):

V.M. Traktyns'ka ◽

M.Ye. Tkachenko

Keyword(s):

Linear Functional ◽

Continuous Functional ◽

Bounded Linear ◽

Linear Continuous Functional ◽

Bounded Linear Functional

The questions of the characterization of the best approximant in spaces with mixed integral metric with weight were considered in this article. The general form of a bounded linear functional and the criterion of best approximant in these spaces are obtained.

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The characterization of the best approximant for the multivariable functions in the space $L_{p_1,..,p_n;\Omega }$

Researches in Mathematics ◽

10.15421/241913 ◽

2020 ◽

Vol 27 (2) ◽

pp. 36

Author(s):

M.Ye. Tkachenko ◽

V.M. Traktynska

Keyword(s):

Linear Functional ◽

Bounded Linear ◽

Bounded Linear Functional

The questions of the characterization of the best approximant in spaces of multivariable functions with mixed integral metric with weight were considered in this article. The general form of a bounded linear functional and the criterion of the best approximant in these spaces are obtained.

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Existence of solutions of extremal problems in H1

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500005034 ◽

1991 ◽

Vol 34 (1) ◽

pp. 99-112 ◽

Cited By ~ 3

Author(s):

Takahiko Nakazi

Keyword(s):

Hardy Space ◽

Linear Functional ◽

Existence Of Solutions ◽

Bounded Function ◽

Hankel Operators ◽

Extremal Problems ◽

Closed Unit Ball ◽

Continuous Linear ◽

Continuous Linear Functional

An essentially bounded function on the unit circle gives a continuous linear functional on the Hardy space H1. In this paper we study when there exists at least one function which attains its norm. We apply the results to an interpolation problem, Hankel operators and a characterization of exposed points of the closed unit ball of H1.

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