Let H (B) denote the space of all holomorphic functions on the unit ball B. Let u is an element of H(B) and phi be a holomorphic self-map of B. In this paper, we investigate the boundedness and compactness of the weighted composition operator uC(phi) from the general function space F(p, q, s) to the weighted-type space H(mu)(infinity) in the unit ball. Copyright (C) 2009 Xiangling Zhu.
In this paper, the variations of both subunitary polar factors and Hermitian positive semidefinite polar factors in the polar decomposition are studied. New perturbation bounds of both polar factors are given without the restriction that A and its perturbed matrix 脙 have the same rank. These improve recent results.
Cardinali, I
Lunardon, G
Polverino, O
Trombetti, R
In this paper we prove that the projections along reguli of a translation spread of the classical generalized hexagon H(q) are translation ovoids of Q(4, q). As translation ovoids of Q(4, 2(r)) are elliptic quadrics, this forces that all translation spreads of H(2(r)) are semi-classical, By representing H(q) as a coset geometry, we obtain a characterization of a translation spread in terms of a set of points of P G (3, q) which belong to imaginary chords of a twisted cubic and we construct a new example of a semi-classical spread of H(2(r)). Finally, we study the semi-classical locally Hermitian 1-systems of Q(6, q) which are spreads of Q(-) (5, q). (C) 2002 Elsevier Science Ltd. All rights reserved.
In this paper, we obtain atomic decompositions for the spaces H1,q, 1 < q < ∞ (this case has not been considered earlier) and show that a multiplier that satisfies the condition of the Marcinkiewicz theorem acts from the space H1 into H1,∞. Bibliography: 5 titles.
In this paper, we define the normalized spherical transform associated with the generalized Gelfand pair (U(p,q),H (n) ), where H (n) is the Heisenberg group 2n + 1-dimensional and p+q=3Dn. We show that the normalized spherical transform of a Schwartz function f on H (n) restricted to the spectrum of the Gelfand pair (U(n),H (n) ) is the Gelfand transform of a radial Schwartz function g on H (n) . Moreover, by the Godement-Plancherel inversion formula the function g can be recovered explicitly from F-(f) .
Bader and Lunardon found a model for the dual of the split Cayley hexagon H(q), q odd and not a power of 3, using a twisted cubic in PG(3, q). We propose a slightly modified version of this model which also works if q is a power of 3, and discuss the connection with a model for the dual of the twisted triality hexagon H(q 3, q) described by Lunardon
Bader and Lunardon found a model for the dual of the split Cayley hexagon H(q), q odd and not a power of 3, using a twisted cubic in PG(3, q). We propose a slightly modified version of this model which also works if q is a power of 3, and discuss the connection with a model for the dual of the twisted triality hexagon H(q(3), q) described by Lunardon. (C) 2003 Elsevier Science (USA). All rights reserved.
Dragan, M
Dixon, SJ
Jaworski, E
Chan, TS
O'Brien, PJ
Wilson, JX
Ascorbate is an important antioxidant in the brain. Astrocytes are capable of recycling ascorbate by taking up and then reducing its oxidation product dehydroascorbic acid (DHAA) using reducing equivalents derived from NAD(P)H. Astrocytes also contain NAD(P)H-dependent quinone reductases, such as NAD(P)H:quinone oxidoreductase (NQO1), which are capable of reducing coenzyme Q and its analogs. Short-chain coenzyme Q analogs have been proposed as therapeutic agents for neurodegenerative illnesses, but they may cause oxidative stress by non-enzymatic redox cycling or enzyme-dependent depletion of NAD(P) H. Therefore, we tested the hypothesis that the short-chain coenzyme Q analog coenzyme Q(1) (CoQ(1), ubiquinone-5) decreases intracellular NAD(P)H levels in astrocytes and impairs the ability of these cells to replace extracellular DHAA with ascorbate (i.e., ascorbate recycling). We observed that CoQ(1) inhibited the production of intra- and extracellular ascorbate by primary rat astrocytes incubated with DHAA in glucose-free medium. Reduction of CoQ(1) to CoQ(1)H(2) by astrocytes was partially blocked by the NQO1 inhibitor dicumarol but was not affected by DHAA. The inhibition of ascorbate recycling by CoQ(1) was attenuated by dicumarol and was abolished by glucose. CoQ(1) lowered intracellular levels of reactive oxygen species, as measured by oxidation of 2',7'-dichlorofluorescin but also produced marked decreases in the concentrations of NADH and NADPH. We conclude that in astrocytes CoQ(1) recycling depletes NAD(P)H and inhibits ascorbate recycling when glucose metabolism is limited. Because DHAA can cause cell-lethal oxidative stress in neurons and ascorbate produced by astrocytes may be neuroprotective, coenzyme Q analogs may adversely affect brain function through this novel mechanism. (c) 2006 Elsevier B.V. All rights reserved.
The authors give an upper bound of the essential norms of composition operators between Hardy spaces of the unit ball in terms of the counting function in the higher dimensional value distribution theory defined by Professor S. S. Chern. The sufficient condition for such operators to be bounded or compact is also given.