As new applications of Schrödinger type inequalities obtained by Jiang (J. Inequal. Appl. 2016: Article ID 247, 2016) in the Schrödingerean Hardy space, we not only obtain the representation of Schrödingerean harmonic functions but also give a sufficient and necessary condition between the Schrödingerean distributional function and its derivative in the Schrödingerean Hardy space.

Techniques of constrained approximation are used to recover solutions to elliptic partial differential equations from incomplete and corrupted boundary data. The approach involves the use of generalized Hardy spaces of functions whose real and imaginary parts are related by formulae similar to the Cauchy–Riemann equations. A prime motivation for this is the modelling of plasma confinement in a ...

Abstract In this paper, we completely characterize the boundedness and compactness of Volterra integration operators $J_{g}$ J g acting from Hardy-type tent spaces HT q , α </mm...

We prove an optimal Hardy inequality for the fractional Laplacian on the half-space. 1. Main result and discussion Let 0 < α < 2 and d = 1, 2, . . .. The purpose of this note is to prove the following Hardy-type inequality in the half-space D = {x = (x1, . . . , xd) ∈ R : xd > 0}. Theorem 1. For every u ∈ Cc(D), (1) 1 2 ∫

The main objective of this paper is to prove Hilbert-type and Hardy-Hilbert-type inequalities with a general homogeneous kernel, thus generalizing a result obtained in [Namita Das and Srinibas Sahoo, A generalization of multiple Hardy-Hilbert’s integral inequality, Journal of Mathematical Inequalities, 3(1), (2009), 139–154].

The Brudnyi-Krugljak theorem on the if-divisibility of Gagliardo couples is derived by elementary means from earlier results of LorentzShimogaki on equimeasurable rearrangements of measurable functions. A slightly stronger form of Calderón's theorem describing the Hardy-LittlewoodPólya relation in terms of substochastic operators (which itself generalizes the classical Hardy-Littlewood-Pólya re...

We consider approximation of L p functions by Hardy functions on subsets of the circle, for 1 p < 1. After some preliminaries on the possibility of such an approximation which are connected to recovery problems of the Carleman type, we prove existence and uniqueness of the solution to a generalized extremal problem involving norm constraints on the complementary subset. problems in Hardy spaces.

In these lectures we give an overview of the circle method introduced by Hardy and Ramanujan at the beginning of the twentieth century, and developed by Hardy, Littlewood and Vinogradov, among others. We also try to explain the main difficulties in proving Goldbach’s conjecture and we give a sketch of the proof of Vinogradov’s three-prime Theorem.

We give general estimates for the approximation numbers of composition operators on the Hardy space on the ball Bd and the polydisk D . Mathematics Subject Classification 2010. Primary: 47B33 – Secondary: 32A07 – 32A35 – 32A70 – 46E22 – 47B07 Key-words. approximation numbers; bounded symmetric domain; composition operator; Hardy space; polydisk; Reinhardt domain; several complex variables