Biomedical subjects
Publications and source records attributed to E M Stein.
We show that the ratios (A(u)/N(u))(k)A(u) and (N(u)/A(u))(k)N(u) have L(p) norms equivalent with the H(p) norm of u. Here A(u) is the Lusin area integral and N(u) is the nontangential maximal function.
One hundred fifty-eight elderly persons living in retirement hotels and apartments were classified by being receivers or givers of help to their neighbors into four groups: givers, getters, both (GG), or neither (NGG). The aim was to determine whether the groups differed in personal characteristics, physical functioning, or psychologic adjustment at baseline and six months later. The groups did not differ in personal characteristics. The NGG group (N = 55) functioned significantly less well, both physically and psychosocially. At six months, with baseline scores adjusted, the givers had fewer illnesses and the GG group had better self-esteem. Thus, subjects did not change significantly in other variables. Efforts to enhance the ability of the NGG group to form social networks, if applied cautiously, may help to improve their overall adjustment.
We study several notions of distance and ball on the boundary of domains of finite type in C(n). We use these notions to develop a theory of maximal functions and area integrals for functions holomorphic in such domains.
We show that the H(p) spaces on the bi-disc can be characterized in terms of either the nontangential maximal function and the area integral or their probabilistic analogues resulting by introducing two-time Brownian motion (i.e., the martingale maximal function) and the corresponding square function.
We describe a class of pseudo-differential operators and their singular integral realizations and show how these may be used to give precise estimates in various function spaces. Application will be given in particular to several situations in which subelliptic estimates arise for partial differential equations.
Let {theta(j)} be a lacunary sequence going to zero. Let [Formula: see text]. Define [Formula: see text]. We prove [Formula: see text].
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Let t --> gamma(t), 0 </= t </= 1, be a smooth curve in IR(n). Define the maximal function [unk](f) by [unk](f)(x) = sup(0<h</=1) (1/h) (0) (h) f(x - gamma(t)) dt. We state conditions under which parallel[unk](f) parallel(p) </= A(p) parallelf parallel(p), for 1 < p </= infinity.
Let [unk](f)(x) denote the supremum of the averages of f taken over all (surfaces of) spheres centered at x. Then f --> [unk](f) is bounded on L(p)(R(n)), whenever p > n/(n - 1), and n >/= 3.
Let t --> gamma(t) be a homogeneous curve in R(n). For suitable f, define [unk](f)(x) = sup(h > 0)|(1/h) [unk](0) (h)f(x - gamma(t)) dt|. Then parallel[unk](f) parallel(p) </= A(p) parallelf parallel(p), 1 < p </= infinity.
Let u be a harmonic function on a symmetric space which is the Poisson integral of a function f in L(p), 1 </= p </= infinity. Then u converges restrictedly and admissibly to f almost everywhere. This result is proved by obtaining an appropriate maximal theorem which takes into account the structure of the Poisson kernel.
The intertwining operators that have been constructed for all the series of unitary representations appearing in the Plancherel formula of a connected real semisimple Lie group of matrices are given a new normalization and then applied in two ways. The first is to obtain dimension formulas for the commuting algebras of the unitary representations in question. The second is to establish the existence of complementary series. These bear the same relationship to the unitary representations under study that the complementary series found earlier bear to the principal series.
We find the necessary and sufficient conditions for the local solvability of Lewy's equation, ([unk]/[unk]z + īz [unk]/[unk]t) u = f. If R(3) is realized as the boundary of the generalized "upper-half-space" in C(2), then the conditions are, near a point P [unk] R(3), the analytic continuability of the Cauchy-Szegö integral of f past P. In case the sufficient condition is satisfied, solutions are found that satisfy optimal regularity properties. Various generalizations are also given.
To evaluate the effect of different levels of arterial oxygen content on hemodynamic parameters during exercise nine subjects performed submaximal bicycle or treadmill exercise and maximal treadmill exercise under three different experimental conditions: 1) breathing room air (control); 2) breathing 50% oxygen (hyperoxia); 3) after rebreathing a carbon monoxide gas mixture (hypoxia). Maximal oxygen consumption (Vo2 max) was significantly higher in hyperoxia (4.99 1/min) and significantly lower in hypoxia (3.80 1/min) than in the control experiment (4.43 1/min). Physical performance changes in parallel with Vo2 max. Maximal cardiac output (Qmax) was similar in hyperoxia as in control but was significantly lower in hypoxia mainly due to a decreased stroke volume. A correlation was found between Vo2 max and transported oxygen, i.e., Cao2 times Amax, thus suggesting that central circulation is an important limiting factor for human maximal aerobic power. During submaximal work HR was decreased in hyperoxia and increased in hypoxia. Corresponding Q values were unchanged except for a reduction during high submaximal exercise in hyperoxia.
Let G be a real noncompact semi-simple Lie group with finite center and K a maximal compact sub-group. The symmetric space M = G/K carries a measure invariant under the action of G. The operators which map L(p)(M) continuously into itself and commute with the action of G, can be easily characterized when p = 2 or p = 1. This note gives some results on "singular integrals" which map L(p) into itself (1 < p < + infinity).
The intertwining operators for nonunitary principal series representations of a real semisimple Lie group are used to construct intertwining operators for all the series of unitary representations appearing in the Plancherel formula. The resulting machinery reduces computations with Harish-Chandra's c-functions and the Plancherel measure to computations with those c-functions and measures obtained from a minimal parabolic subgroup.
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