Interpolation in variable exponent spaces

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale

Anisotropic Singular Integrals in Product Spaces

Let $A_i$ for $i=1, 2$ be an expansive dilation, respectively, on ${\mathbb R}^n$ and ${\mathbb R}^m$ and $\vec A\equiv(A_1, A_2)$. Denote by {\mathcal A}_\infty(\rnm; \vec A) the class of Muckenhoupt weights associated with $\vec A$. The authors introduce a class of anisotropic singular integrals on $\mathbb R^n\times\mathbb R^m$, whose kernels are adapted to $\vec A$ in the sense of Bownik and have vanishing moments defined via bump functions in the sense of Stein. Then the authors establish the boundedness of these anisotropic singular integrals on $L^q_w(\mathbb R^n\times\mathbb R^m)$ with $q\in(1, \infty)$ and $w\in\mathcal A_q(\mathbb R^n\times\mathbb R^m; \vec A)$ or on $H^p_w(\mathbb R^n\times\mathbb R^m; \vec A)$ with $p\in(0, 1]$ and $w\in\mathcal A_\infty(\mathbb R^n \times\mathbb R^m; \vec A)$. These results are also new even when $w=1$.Comment: Sci. China Math., to appea

Seasonal variation of non-shivering thermogenesis (NST) during mild cold exposure

Background: The physiological function of non-shivering thermogenesis (NST) has been investigated in recent years, and some studies have discussed the importance of NST with respect to human cold adaptation. The present study aimed to clarify individual and seasonal variations in NST that occurred as a result of mild cold exposure.Methods: Seventeen male university students participated in the present study during summer and winter. The climate chamber used was programmed so that ambient temperature dropped from 28°C to 16°C over an 80-min period. Physiological parameters of test subjects were recorded during the experiments.Results: Increases in oxygen intake (VO2) during cold exposure were significantly greater without shivering in winter than they were in summer. Respiratory exchange ratio (RER) was significantly lower during thermoneutral baseline and cold exposure in winter than it was during the same periods in summer. In addition, there was a significant negative correlation between ΔVO2 and ΔRER.Conclusions: Increase of VO2 without shivering indicated increase of NST, and decrease of RER depends on the metabolization of fat in winter. These results suggested that NST activity was activated by seasonal acclimatization, and individual variation of NST depends on individual variation of fat metabolism

Thermal, Cardiac and Adrenergic Responses to Repeated Local Cooling

Summary The aim of this study was to ascertain whether repeated local cooling induces the same or different adaptational responses as repeated whole body cooling. Repeated cooling of the legs (immersion into 12 °C water up to the knees for 30 min, 20 times during 4 weeks = local cold adaptation -LCA) attenuated the initial increase in heart rate and blood pressure currently observed in control subjects immersed in cold water up to the knees. After LCA the initial skin temperature decrease tended to be lower, indicating reduced vasoconstriction. Heart rate and systolic blood pressure appeared to be generally lower during rest and during the time course of cooling in LCA humans, when compared to controls. All these changes seem to indicate attenuation of the sympathetic tone. In contrast, the sustained skin temperature in different areas of the body (finger, palm, forearm, thigh, chest) appeared to be generally lower in LCA subjects than in controls (except for temperatures on the forehead). Plasma levels of catecholamines (measured 20 and 40 min after the onset of cooling) were also not influenced by local cold adaptation. Locally cold adapted subjects, when exposed to whole body cold water immersion test, showed no change in the threshold temperature for induction of cold thermogenesis. This indicates that the hypothermic type of cold adaptation, typically occurring after systemic cold adaptation, does not appear after local cold adaptation of the intensity used. It is concluded that in humans the cold adaptation due to repeated local cooling of legs induces different physiological changes than systemic cold adaptation