framework for John Nirenberg inequalities and applications to Hardy spaces Frédéric Bernicot CNRS Laboratoire Paul Painlevé Université Lille 1 59655 Villeneuve d’Ascq Cedex, France [email protected] Jiman Zhao ∗ School of Mathematical Sciences, Beijing Normal University Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P.R. China jzhao...

bream (abramis brama orientalis) is one of the most commercially valuable fish in the caspian sea. the aim of this study was to compare levels of genetic polymorphism between wild and farmed bream populations using seven microsatellite loci. genetic diversity was investigated by studying samples collected from two regions; chaboksar and the artificial propagation center of guilan province. alle...

There are well-known examples of dynamical systems for which the Birkhoff averages with respect to a given observable along some or all of the orbits do not converge. It has been suggested that such orbits could be classified using higher order averages. In the case of a bounded observable, we show that a classical result of G.H. Hardy implies that if the Birkhoff averages do not converge, then...

We produced a set of pseudoisochromatic plates for determining individual color-difference thresholds to assess test performance and test properties, and analyzed the results. We report a high test validity and classification ability for the deficiency type and severity level [comparable to that of the fourth edition of the Hardy-Rand-Rittler (HRR) test]. We discuss changes of the acceptable ch...

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The goal of this paper is to give some information about the following question, posed by Andreas Weiermann (private communication). Is it true that for every β, γ < ε0 there exist α so that whenever A is α–large, A satisfies some inessential assumption, say min(A) ≥ 2, and G : A → β is such that ∀a ∈ A psn(G(a)) ≤ a there must exist γ–large C ⊆ A on which G is nondecreasing. Here ε0 is the sma...

This note is devoted to several inequalities deduced from a special form of the logarithmic Hardy-LittlewoodSobolev, which is well adapted to the characterization of stationary solutions of a Keller-Segel system written in self-similar variables, in case of a subcritical mass. For the corresponding evolution problem, such functional inequalities play an important role for identifying the rate o...

Despite our recent commentary on the article by Resende and Weber, the authors still seem to believe that Sir Charles Bell (1774-1842) himself was affected by facial paralysis. They came to this erroneous conclusion from a paper by Jongkees and by “neurological examination of the photograph of Sir Charles Bell” (Fig 1). However, had they taken the effort to check Jongkees’ German translation wi...

In this paper, we reconstruct the Hardy-Littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. An open problem is raised.

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...