One-sided maximal functions and Hp

AbstractLet N be the nontangential maximal function of a function u harmonic in the Euclidean half-space Rn × (0, ∞) and let N− be the nontangential maximal function of its negative part. If u(0, y) = o(y−n) as y → ∞, then ∥N∥p ⩽ cp ∥N−∥p, 0 < p < 1, and more. The basic inequality of the paper (Theor. 2.1) can be used not only to derive such global results but also may be used to study the behavior of u near the boundary. Similar results hold for martingales with continuous sample functions. In addition, Theorem 1.3 contains information about the zeros of u. For example, if u belongs to Hp for some 0 < p < 1, then every thick cone in the half-space must contain a zero of u

Thermodynamics and Universality for Mean Field Quantum Spin Glasses

We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin glass models to answer analogous questions about quantum models.Comment: 17 page

Association Between Bilirubin, Atazanavir, and Cardiovascular Disease Events Among People Living With HIV Across the United States

Objective: Bilirubin is an antioxidant that may suppress lipid oxidation. Elevated bilirubin is associated with decreased cardiovascular events in HIV-uninfected populations. We examined these associations in people living with HIV (PLWH). Methods: Potential myocardial infarctions (MIs) and strokes were centrally adjudicated. We examined MI types: type 1 MI (T1MI) from atherosclerotic plaque instability and type 2 MI (T2MI) in the setting of oxygen demand/supply mismatch such as sepsis. We used multivariable Cox regression analyses to determine associations between total bilirubin levels and outcomes adjusting for traditional and HIV-specific risk factors. To minimize confounding by hepatobiliary disease, we conducted analyses limited to bilirubin values <2.1 mg/dL; among those with fibrosis-4 values <3.25; and among everyone. We repeated analyses stratified by hepatitis C status and time-updated atazanavir use. Results: Among 25,816 PLWH, there were 392 T1MI and 356 T2MI during follow-up. Adjusted hazard ratios for the association of higher bilirubin levels with T1MI were not significant. Higher bilirubin levels were associated with T2MI. By contrast, among PLWH on atazanavir, higher bilirubin levels were associated with fewer T2MI (hazard ratio 0.56:0.33-1.00). Higher bilirubin levels among those on atazanavir were associated with fewer T1MI combined with ischemic stroke. Limitations: Analyses were conducted with total rather than unconjugated bilirubin. Conclusions: Among PLWH, higher bilirubin levels were associated with T2MI among some subgroups. However, among those on atazanavir, there was a protective association between bilirubin and T2MI. These findings demonstrate different associations between outcomes and elevated bilirubin due to diverse causes and the importance of distinguishing MI types

Types of Stroke among People Living with HIV in the United States

Background: Most studies of stroke in people living with HIV (PLWH) do not use verified stroke diagnoses, are small, and/or do not differentiate stroke types and subtypes.Setting: CNICS, a U.S. multisite clinical cohort of PLWH in care.Methods: We implemented a centralized adjudication stroke protocol to identify stroke type, subtype, and precipitating conditions identified as direct causes including infection and illicit drug use in a large diverse HIV cohort.Results: Among 26,514 PLWH, there were 401 strokes, 75% of which were ischemic. Precipitating factors such as sepsis or same-day cocaine use were identified in 40% of ischemic strokes. Those with precipitating factors were younger, had more severe HIV disease, and fewer traditional stroke risk factors such as diabetes and hypertension. Ischemic stroke subtypes included cardioembolic (20%), large vessel atherosclerosis (13%), and small vessel (24%) ischemic strokes. Individuals with small vessel strokes were older, were more likely to have a higher current CD4 cell count than those with cardioembolic strokes and had the highest mean blood pressure of the ischemic stroke subtypes.Conclusion: Ischemic stroke, particularly small vessel and cardioembolic subtypes, were the most common strokes among PLWH. Traditional and HIV-related risk factors differed by stroke type/subtype. Precipitating factors including infections and drug use were common. These results suggest that there may be different biological phenomena occurring among PLWH and that understanding HIV-related and traditional risk factors and in particular precipitating factors for each type/subtype may be key to understanding, and therefore preventing, strokes among PLWH