in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

Abstract Let $$\Omega $$ Ω be a bounded domain in $${{\mathbb {R}}}^N$$ R N with $$C^2$$ C 2 boundary and let $$K\subset \partial \Omega K ⊂ ∂ ei...

This paper discusses generalization bounds for complex data learning which serve as a theoretical foundation for complex support vector machine (SVM). Drawn on the generalization bounds, a complex SVM approach based on the Szegő kernel of the Hardy space H(D) is formulated. It is applied to the frequency-domain identification problem of discrete linear time-invariant system (LTIS). Experiments ...

A class of fractional derivative operators (with the Appell hypergeometric function in the kernel) is used here to define a new subclass of analytic functions and a coefficient bound inequality is established for this class of functions. Also, an inclusion theorem for a class of fractional integral operators involving the Hardy space of analytic functions is proved. The concluding remarks brief...

Hardy persons are hypothesized to be resistant to stress-induced illness, because of their adaptive cognitive style and a subsequently reduced level of physiological arousal. We assessed the cognitive and physiological responses of high and low hardy male undergraduates to a challenging task under high and low evaluative threat. As predicted, hardy subjects endorsed more positive self-statement...

This tutorial paper discusses a number of classical interpolation results from the theory of Hardy spaces, and stresses the role played by reproducing kernels. Next, the reproducing kernel thesis is presented in several different contexts. Some basics of the theory of linear systems are described, leading into two applications of the abstract results: the first is in the recovery of functions f...

* Correspondence: larserik@ltu.se Department of Engineering Sciences and Mathematics, LuleåUniversity of Technology SE 971 87 Luleå, Sweden Full list of author information is available at the end of the article Abstract First we present and discuss an important proof of Hardy’s inequality via Jensen’s inequality which Hardy and his collaborators did not discover during the 10 years of research ...

We consider Carleson measures, Hankel matrices, and interpolation of values on certain reproducing kernel Hilbert spaces which we call the diameter spaces. We begin by reviewing results for the classical Hardy space which we denote DAH1 and its associated diameter space. Our n−dimensional analog of the Hardy space is the Drury-Arveson-Hardy space, DAHn, a space of holomorphic functions on the u...