In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an upper bound on the mean curvature of a constant mean curvature surface homologous to a subset of the interior boundary components. This bound allows us to find a maximizer for the constant mean curvature of a surface ...

We show that there is a measure μ, defined on the hyperbolic plane and with polynomial growth, such that the centered maximal operator associated to μ does not satisfy weak type (1, 1) bounds.

For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a m...

We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of f, M f, by an expression involving the nonincreasing rearrangement of f. This estimate is used to obtain necessary and suucient conditions for the boundedness of M between classical Lorentz spaces.

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability b...

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