Let P be a linear, elliptic second order symmetric operator, with an associated quadratic form q, and let W be a potential such that the Hardy inequality λ0 ∫ Ω Wu 2 ≤ q(u) holds with (non-negative) best constant λ0. We give sufficient conditions so that the spectrum of the operator 1 W P is [λ0,∞). In particular, we apply this to several well-known Hardy inequalities: (improved) Hardy inequali...

is part of that broader field of experimental pathology to which all medical sciences belong". This is reflected in the thirty important years Hardy spent as Chairman and Professor in the Department of Surgery at the University of Mississipi in Jackson, where he divided his activities among surgical practice, teaching, and research. The period of his memoirs saw advances in surgical pathology a...

is part of that broader field of experimental pathology to which all medical sciences belong". This is reflected in the thirty important years Hardy spent as Chairman and Professor in the Department of Surgery at the University of Mississipi in Jackson, where he divided his activities among surgical practice, teaching, and research. The period of his memoirs saw advances in surgical pathology a...

The aim of this study was to investigate allele frequencies at the CSN1S2 locus in two Chinese dairy goat breeds and the effects of its variation on dairy goat economic traits. Seven hundred and eight goats from Xinong Saanen (XS, n = 268) and Guanzhong (GZ, N = 440) breeds were selected. The milk samples of 268 XS goats were collected during the middle of lactation, body size parameters (708 g...

The main purpose of this paper is to briefly review the earlier works of multiparameter Hardy space theory and boundedness of singular integral operators on such spaces defined on product of Euclidean spaces, and to describe some recent developments in this direction. These recent works include discrete multiparameter Calderón reproducing formulas and Littlewood-Paley theory in the framework of...

We survey polynomial inequalities obtained via coefficient multipliers, for norms defined by the contour or the area integrals over the unit disk. Special attention is devoted to the Szegő composition and the inequalities related to Mahler’s measure. We also consider a new height on polynomial spaces defined by the integral over the normalized area measure on the unit disk. This natural analog ...

This paper tries to find out five poets’ (Thomas Hardy, Wilde, Browning, Yeats, and Tagore) differences and similarities through analyzing their works on nineteenth Century by using natural language understanding technology and word vector model. Firstly, we collect enough poems from these five poets, build five corpus respectively, and calculate their high-frequency words, by using Natural Lan...

* Correspondence: [email protected] 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 ...

In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spa...