Multilinear interpolation between adjoint operators

Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L^q estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak L^q estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak L^q has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441).     

Interpolation of Bilinear Operators Between Quasi-Banach Spaces

We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-Lozanovsky spaces, and Lorentz-Zygmund spaces are presented. The author is supported by the National Science Foundation under grant DMS 0099881. The author is supported by KBN Grant 1 P03A 013 26.     

Agents facilitating the electric field-induced fusion of intact rabbit erythrocytes

In the recent years, the role of specific membrane active agents in the electrofusion process has started to draw attention, and it has been found that the presence of various substances in the cell medium can affect the fusion process either in a positive or negative way. In this work, the effect of several proteins, bivalent cations and antibiotics was tested with respect to their ability to protect intact erythrocytes from hemolysis and facilitate the fusion process. The effect of different sugars was also studied. Among the different proteins, pronase and proteinase were found to be the most effective. With respect to bivalent cations, Ca2+ and Mn2+ were more effective while Mg2+ was less important. From the antibiotics, penicillin caused a negative effect while streptomycin acted positively. Finally, glucose medium was found to be the most effective compared to all sugars tested. The results indicated that there are strong differentiations of the induced effects caused by each substance, and some possible mechanisms of action of these agents on the erythrocyte membrane were discussed.     

Morphological changes in the cellulose and lignin components of biomass occur at different stages during steam pretreatment

Morphological changes to the different components of lignocellulosic biomass were observed as they occurred during steam pretreatment by placing a pressure reaction cell in a neutron beam and collecting time-resolved neutron scattering data. Changes to cellulose morphology occurred mainly in the heating phase, whereas changes in lignin morphology occurred mainly in the holding and cooling phases. During the heating stage, water is irreversibly expelled from cellulose microfibrils as the elementary fibrils coalesce. During the holding phase lignin aggregates begin to appear and they increase in size most noticeably during the cooling phase. This experiment demonstrates the unique information that in situ small angle neutron scattering studies of pretreatment can provide. This approach could be useful in optimizing the heating, holding and cooling stages of pretreatments to allow the exact size and nature of lignin aggregates to be controlled in order to enhance enzyme accessibility to cellulose and therefore the efficiency of biomass conversion.     

Multilinear Calderón-Zygmund Theory

A systematic treatment of multilinear Calderón-Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, a multilinear T1 theorem, and a variety of results regarding multilinear multiplier operators.     

Validation of a novel, fully automated high throughput high-performance liquid chromatographic/tandem mass Spectrometric method for quantification of pantoprazole in human plasma

An automated high-throughput HPLC/MS/MS method was developed for the quantitative determination of pantoprazole in human plasma. Only 100 microL plasma was placed in 2.2 mL 96 deep-well plates, and both pantoprazole and omeprazole (IS) were extracted from human plasma by liquid-liquid extraction, using diethyl ether-dichloromethane (70:30, v/v) as the organic solvent. Robotic liquid-handling workstations were used for all liquid transfer and solution preparation steps and resulted in a short sample preparation time. After vortexing, centrifugation, and freezing, the supernatant organic solvent was evaporated and reconstituted in a small volume of reconstitution solution. Sample analysis was performed by utilizing the combination of RP-HPLC/MS/MS, with positive-ion electrospray ionization and multiple reaction monitoring detection. The chromatographic run time was set at 1.8 min with a flow rate of 0.6 mL/min on a Nucleosil octylsilyl (C8) analytical column. The method was proven to be sensitive, specific, accurate, and precise for the determination of pantoprazole in human plasma. The method was applied to a bioequivalence study after per os administration of a 40 mg pantoprazole gastric retentive tablet.     

Weighted norm inequalities for maximally modulated singular integral operators

We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good- method of Coifman and Fefferman [CF] and an alternative method employing the sharp maximal operator. As an application we obtain new weighted and vector-valued inequalities for the Carleson operator proving that it is controlled by a natural maximal function associated with the Orlicz space L(log L)(log log log L). This control is in the sense of a good- inequality and yields strong and weak type estimates as well as vector-valued and weighted estimates for the operator in question.Mathematics Subject Classification (2000): 42B20, 42B25The first author is supported by the National Science Foundation under grant DMS 0099881.Part of this work was carried out while the second author was a Postdoctoral Fellow at University of Missouri-Columbia. The second author would like to thank this department for its support and hospitality.The second and the third authors are partially supported by MCYT Grant BFM2001-0189.     

Distributional estimates for the bilinear Hilbert transform

We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results yield all known L^p bounds for the bilinear Hilbert transform and provide new restricted weak type endpoint estimates on L^p1 × L^p2 when either 1/p₁ + 1/p₂ = 3/2 or one of p₁, p₂ is equal to 1. As a consequence of this work we also obtain that the square root of the bilinear Hilbert transform of two characteristic functions is exponentially integrable over any compact set.     

Multilayer metal/metal-oxide diffractive structure for photonic temperature sensing

We designed and fabricated multilayer metal/metal-oxide surface relief diffractive grating structures by growing alternating Pt and SnO(x) layers. Optical interrogation at 633 nm reveals the temperature dependence of their reflection and transmission diffractive effects. This function is explored here in the context of a remote, spatially localized, photonic temperature sensing operation, achieving sensitivity of 10% per °C for the zeroth-order in the transmission mode. The experimental demonstration is found to be in good agreement with the results of rigorous coupled wave analysis of the composite metal/metal-oxide element.