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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 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)
Excessive subconjunctival scarring is the main reason of failure of glaucoma filtration surgery. We analyzed conjunctival and systemic gene expression patterns after non penetrating deep sclerectomy (NPDS). To find expression patterns related to surgical failure and their correlation with the clinical outcomes. This study consisted of two consecutive(More)