Timothy A. Gillespie

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In this paper we establish dimension free Lp(Rn, |x|α) norm inequalities (1 < p < ∞) for the oscillation and variation of the Riesz transforms in Rn. In doing so we find Ap−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 , μ) will(More)
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. (More)
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 ≤ p < ∞, there exists Cp > 0 such that ‖ X k rkSIkf‖Lp Lp([0,1])(R) ≤ Cp‖f‖Lp(R), where the rk’s are the Rademacher functions. In this note we prove that, given a compact connected abelian group G with dual group Γ and p in the(More)
Some intriguing discoveries were made concerning the collision-activated dissociation behavior of the derivatized carboxylate anions of PGE2 and PGF2α. The carboxylate anion [MPFB](-) formed from electron-capture negative chemical ionization of the pentafluorobenzyl ester-trimethylsilyl derivative of PGF2α showed little fragmentation under typical collision(More)
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 _• p • c•. We show that under appropriate circumstances the representation R will transfer to X the bounds for square functions defined by sequences of(More)