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We study weak-type (1, 1) weighted inequalities for the fractional integral operator I α. We show that the fractional maximal operator M α controls these inequalities when the weight is radially decreasing. However, we exhibit some counterexamples which show that M α is not appropriate for this control on general weights. We do provide, nevertheless, some… (More)
We study the boundedness of bilinear convolutions operators with positive kernels. We prove both necessary and sufficient conditions and, by means of several counterexamples we show that near the endpoints the behavior of positive translation-invariant bilinear operators can be quite different than that of positive linear ones.
Peroxynitrite (ONOO(-)) is a potent oxidant formed by the nonenzymatic reaction between superoxide anion (O(2)(*-)) and nitric oxide (NO*) in a one-to-one stoichiometry. Accumulated evidence suggests that endothelial dysfunction coincides with an enhanced NO* synthase expression and O(2)(*-) production, facilitating ONOO(-) formation. In vivo, formation of… (More)
Most cyanobacteria take up nitrate or nitrite through a multisubunit ABC transporter (ATP-binding cassette) located in the cytoplasmic membrane. Nitrate and nitrite transport activity is instantaneously blocked by the presence of ammonium in the medium. Previous biochemical studies reported the existence of phosphorylation/dephosphorylation events of the… (More)
PURPOSE To evaluate a limbal stem cell deficiency (LSCD) diagnosis method based on the detection of the MUC5AC transcript by reverse transcription-polymerase chain reaction (RT-PCR) in comparison with the standard diagnostic method based on goblet cell detection by periodic acid-Schiff (PAS)-hematoxylin staining, using samples obtained from corneal… (More)
Endogenous peptides are valuable targets in the analysis of biological processes. The tear film contains proteins and peptides released by the tear duct mucosal cells, including antimicrobial peptides involved in the protection against exogenous pathogens; however, the peptide content of the tear liquid remains poorly characterized. We analyzed naturally… (More)
We introduce a new decreasing rearrangement for functions defined on a homogeneous tree, which enjoys very intuitive and natural properties. The idea is to iterate, with respect to a particular ordering, the usual one dimensional rearrangement on each geodesic. After showing the canonicity of this definition and the axioms of symmetrization, we prove our… (More)
The authors consider fractal measures µ supported on compact sets in R ν , which arise from iteration algorithms that are defined from a given affine system of maps in R ν. Then, they study the possible orthogonal harmonic function systems in L 2 (µ), and, in particular, they give conditions for L 2 (µ) to have an orthonormal harmonic basis. The measure µ… (More)
We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.