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L p -approximation of Jacobians

Jan Malý (1991)

Commentationes Mathematicae Universitatis Carolinae

The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from Cart p ( Ω , 𝐑 m ) is approximated by 𝒞 1 functions strongly in 𝒜 q ( Ω , 𝐑 m ) whenever q < p . An example is shown of a function which is in cart p ( Ω , 𝐑 2 ) but not in cart p ( Ω , 𝐑 2 ) .

Locally solid topologies on spaces of vector-valued continuous functions

Marian Nowak, Aleksandra Rzepka (2002)

Commentationes Mathematicae Universitatis Carolinae

Let X be a completely regular Hausdorff space and E a real normed space. We examine the general properties of locally solid topologies on the space C b ( X , E ) of all E -valued continuous and bounded functions from X into E . The mutual relationship between locally solid topologies on C b ( X , E ) and C b ( X ) ( = ...

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