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Defensive Inequalities

October 2016

October 2016

Authors:

Cara Chellew

McGill University

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A(infinity)(R-n) WEIGHTS AND THE LOCAL MAMMAL OPERATOR

December 2012 · Taiwanese Journal of Mathematics

Let s is an element of (0, 1/2), m(0,) (s) be the local maximal operator of John and Stromberg, and M-0,M- (s) the multi(sub)linear local maximal operator. In this paper, the authors give some characterizations of the weights w(1), ... , w(l) for which the operator M-0,M- (s) is bounded from L-p1(R-n, w(1)) x ... x L-pl(R-n, w(1)) to L-pl(R-n, nu(w) over right arrow) with nu(w) over right arrow = ... [Show full abstract] Pi(l)(k=1) w(k)(p/pk),p(1), ... , pl is an element of (0, infinity) and 1/p = Sigma(1 <= k <= l) 1/pk. A new characterization of A(infinity)(R-n) weights and a characterization of weights w which satisfies W-theta is an element of A(infinity)(R-n) for some theta is an element of (0, infinity), are also obtained.

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On a conjecture of Clark and Ismail

May 2005 · Journal of Approximation Theory

Let phi(m) (x) = -x(m)psi((m))(x), where psi denotes the logarithmic derivative of Euler's gamma function. Clark and Ismail prove in a recently published article that if m is an element of {1, 2,..., 16}, then phi((m))(m) is completely monotonic on (0, infinity), and they conjecture that this is true for all natural numbers m. We disprove this conjecture by showing that there exists an integer ... [Show full abstract] m(0) such that for all m >= m(0) the function phi((m))(m) is not completely monotonic on (0, infinity). (c) 2005 Elsevier Inc. All rights reserved.

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Full-text available

Inequalities for the volume of the unit ball in ℓpn

April 2008 · Filomat

Let B-p(n) = {x is an element of R-n |parallel to x parallel to(p) <= 1} be the unit ball in l(p)(n). We prove the inequalities for the volume of the B-p(n): V-Bpn+1(1/n+1) < V-Bpn(1/n) 2 Gamma(1/p + 1) p root p/n+p VBpn <= VBpn+1 for all n >= 1 and p > 1, where V-Bpn denotes the volumes of B-p(n). Furthermore, we obtain the upper and lower bounds of V-Bpn+1(n/n + 1)/V-Bpn and VpBn+1/V-Bpn. Our ... [Show full abstract] results are generalizations for inequalities in R n proved and refined by G. D. Anderson et al., K. H. Borgwardt, D. A. Klain and G.- C. Rota and H. Alzer.

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Article

Discrete $H^1$-Inequalities for Spaces Admitting M-Decompositions

January 2018 · SIAM Journal on Numerical Analysis

We find new discrete H¹- and Poincaré-Friedrichs inequalities by studying the invertibility of the discontinuous Galkerkin (DG) approximation of the flux for local spaces admitting M-decompositions. We then show how to use these inequalities to define and analyze new, superconvergent hybridizable DG (HDG) and mixed methods for which the stabilization function is defined in such a way that the ... [Show full abstract] approximations satisfy new H¹-stability results with which their error analysis is greatly simplified. We apply this approach to define a wide class of energy-bounded, superconvergent HDG and mixed methods for the incompressible Navier-Stokes equations defined on unstructured meshes using, in two dimensions, general polygonal elements and, in three dimensions, general, flat-faced tetrahedral, prismatic, pyramidal, and hexahedral elements.

Defensive Inequalities

Abstract

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A(infinity)(R-n) WEIGHTS AND THE LOCAL MAMMAL OPERATOR

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Inequalities for the volume of the unit ball in ℓpn

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