This paper proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilber...

Three major techniques for statistically handling LIV are reviewed: (1) regression analysis as proposed by Lacey (ALS); (2) the difference between standardized preand poststimulus scores as proposed by Heath and Oken,and (3) the intuitively appealing per cent change transformations. The proposed criterion of a satisfactory score is: The correlation between the initial level and a properly corre...

Lacey's high school needed her talent and skills. Located in an urban, working-class community, the school was struggling to serve all students well and had failed to make Adequate Yearly Progress for two years running. As a social studies teacher, Lacey had developed considerable skill in teaching with a project-based format during her four years in the classroom, and her students were making ...

S. Hegyi, C. Höhne, K. Kadija, A. Karev, D. Kikola, M. Kliemant, S. Kniege, V.I. Kolesnikov, E. Kornas, R. Korus, M. Kowalski, I. Kraus, M. Kreps, A. László, R. Lacey, M. van Leeuwen, P. Lévai, L. Litov, B. Lungwitz, M. Makariev, A.I. Malakhov, M. Mateev, G.L. Melkumov, C. Meurer, A. Mischke, M. Mitrovski, J. Molnár, St. Mrówczyński, V. Nicolic, G. Pálla, A.D. Panagiotou, D. Panayotov, A. Petri...

We study the operator Hvf(x) := p.v. ∫ 1 −1 f(x− yv(x)) dy y defined for smooth functions on the plane and measurable vector fields v from the plane into the unit circle. We prove that if v has 1+2 derivatives, then Hv extends to a bounded map from L(R) into itself. What is noteworthy is that this result holds in the absence of some additional geometric condition imposed upon v, and that the sm...

leukoencephalopathy and systemic manifestations Anine H. Stam,* Parul H. Kothari,*Aisha Shaikh, Andreas Gschwendter, Joanna C. Jen, Suzanne Hodgkinson, Todd A. Hardy, Michael Hayes, Peter A. Kempster, Katya E. Kotschet, Ingeborg M. Bajema, Sjoerd G. van Duinen, Marion L. C. Maat-Schieman, Paulus T. V. M. de Jong, Marc D. de Smet, Didi de Wolff-Rouendaal, Greet Dijkman, Nadine Pelzer, Grant R. K...

I shall survey some recent results of Auscher, Axelsson and myself, concerning second order elliptic divergence form equations with complex measurable coefficients A that are independent of the transversal coordinate. In particular, we prove that the set of A ∈ L∞(Rn;Cn+1) for which boundary value problems with L2 Dirichlet or Neumann data are well posed, is an open set. This work is based on r...

M. Lacey and C. Thiele proved in [26] (Annals of Math. (1997)) and [27] (Annals of Math. (1999)) that the bilinear Hilbert transform maps L1 × L2 → L boundedly when 1 p1 + 1 p2 = 1 p with 1 < p1, p2 ≤ ∞ and 2 3 < p < ∞. Whether the L estimates hold in the range p ∈ (1/2, 2/3] has remained an open problem since then. In this paper, we prove that the bilinear Hilbert transform does not satisfy an...

To prepare the samples for Transmission Electron Microscopy (TEM) imaging and Atomic Force Microscopy (AFM) measurements, as-grown carbon nanotubes were dispersed in isopropanol and sonicated using HD2200 homogenizer with a power of 20W for 5 minutes. To characterize the nanotubes by HRTEM, a droplet of the suspension was put on a Cu TEM grid with a lacey C film. Alternatively, we deposited a d...

benefit offered by sumatriptan therapy? Cephalalgia 1995; 15(suppl 14):263 12 Fowler PA, Lacey LF, Thomas M, Keene ON, Tanner RJN, Baber NS. The clinical pharmacology, pharmacokinetics and metabolism of sumatriptan. Eur Neurol 1991; 31:291-4. 13 Blau JN. Sumatriptan and the recurrence of migraine. Lancet 1992;340: 1110. 14 Mathew NT. Drug-induced headache. Neurol Clin 1990; 8:903-12. 15 Mathew ...