Displaying similar documents to “On a result by Clunie and Sheil-Small”

Change of variables formula under minimal assumptions

Piotr Hajłasz (1993)

Colloquium Mathematicae

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In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We...

An abstract nonlinear second order differential equation

Jan Bochenek (1991)

Annales Polonici Mathematici

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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.

Carathéodory balls and norm balls in H p , n = z ∈ ℂ n : ∥ z ∥ p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z ∈ ℂ n : ∥ z ∥ p < 1 which are balls with respect to the complex l p norm in ℂ n are those centered at the origin.