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In this paper we establish dimension free Lp(Rn, |x|Î±) norm inequalities (1 < p < âˆž) for the oscillation and variation of the Riesz transforms in Rn. In doing so we find Apâˆ’weighted norm inequalities for the oscillation and the variation of the Hilbert transform in R. Some weighted transference results are also proved. INTRODUCTION Throughout (X,F , Î¼) willâ€¦ (More)

- Barbara J. Riegel, Dale N Glaser, Victor Thomas, I T Gocka, Timothy A. Gillespie
- Heart & lung : the journal of critical care
- 1997

OBJECTIVE
Dependency is frequently mentioned in the literature as a response of patients with cardiac disease. The purpose of this study was to develop and test a measure of dependency occurring in response to a cardiac illness. Illness dependency is defined as the need for emotional protection and social support after a significant change in health.
â€¦ (More)

Let T = {Ts}sâˆˆR be a strongly continuous one-parameter group of positive operators acting on L(Î¼), where Î¼ is a Ïƒ-finite measure and 1 â‰¤ p < âˆž. We develop a weighted ergodic theory associated with T which parallels the classical theory of Ap-weights. A weighted transference principle is obtained in this setting and used to establish dimension free weightedâ€¦ (More)

- Timothy A. Gillespie, JosÃ© L. Torrea, Roberto MaÄ‡Ä±as, rkSIk fâ€–Lp, rkSIkf
- 2005

A well known result by Rubio de Francia asserts that for every finite family of disjoint intervals {Ik} in R, and p in the range 2 â‰¤ p < âˆž, there exists Cp > 0 such that â€– X k rkSIkfâ€–Lp Lp([0,1])(R) â‰¤ Cpâ€–fâ€–Lp(R), where the rkâ€™s are the Rademacher functions. In this note we prove that, given a compact connected abelian group G with dual group Î“ and p in theâ€¦ (More)

- Timothy A. Gillespie, Richard A. Yost
- Journal of the American Society for Massâ€¦
- 1990

Some intriguing discoveries were made concerning the collision-activated dissociation behavior of the derivatized carboxylate anions of PGE2 and PGF2Î±. The carboxylate anion [MPFB](-) formed from electron-capture negative chemical ionization of the pentafluorobenzyl ester-trimethylsilyl derivative of PGF2Î± showed little fragmentation under typical collisionâ€¦ (More)

- C Y Wu-Wang, Josef Neu, Timothy A. Gillespie, Richard A. Yost
- Seminars in perinatology
- 1986

- N. Asmar, EARL BERKSON, Timothy A. Gillespie
- 2004

Abstract. Let G be a locally compact abelian group, and let u --* Ru be a uniformly bounded, strongly continuous representation of G in a closed subspace X of Lp(p), where p is an arbitrary measure and 1 _â€¢ p â€¢ câ€¢. We show that under appropriate circumstances the representation R will transfer to X the bounds for square functions defined by sequences ofâ€¦ (More)