On weak differential inequalities
نویسندگان
چکیده
منابع مشابه
On Inequalities of Weak Type
for every f (x) in L(X) and A > 0 . Conclusions of this sort are called inequalities of weak type, or, where T*f(x) = supn | Tnf(x) | = r*(#, ƒ), that the operator T* is of weak type (p, p). Inequality (1) has often appeared with convergence a.e. in analysis, but a single result of this generality, predicting (1) as a consequence of convergence, had never before been obtained. Indeed, it seems ...
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The following Lemma gives conditions for the existence of a solution of a differential equation which is bounded on the domain R. Lemma 1.1. Given real numbers a < b, if f : (a, b) → R is a continuous, nonvanishing function, and there are some constants C1 > 0, C2 > 0, δ1 ∈ (0, b − a), δ2 ∈ (0, b − a) so that |f(t)| ≤ C1(t − a) for a < t < a + δ1 and |f(t)| ≤ C2(b − t) for b − δ2 < t < b, then ...
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where 0 ≤ s ≤ t ≤ 1 and ⊗ denotes a tensor product. Lyons [17] proved that solutions of stochastic differential equations (SDEs) are continuous functions of the Brownian rough path w(s, t) = ( w(s, t)1, w(s, t)2). We give a precise definition of the Brownian rough path in the next section; see also [18] and [15]. The discontinuity of solutions of SDEs in the uniform convergence topology of w ca...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1965
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-16-2-185-194