Estimates for partial derivatives of vector-valued functions
Hytönen, Tuomas P.
Illinois J. Math., Tome 51 (2007) no. 3, p. 731-742 / Harvested from Project Euclid
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An upper bound for $\|D^{\beta}u\|_q$ in terms of other similar norms $\|D^{\alpha}u\|_p$ is derived for vector-valued test functions $u\in C_c^{\infty}(\mathbf{R}^n,X)$, where $X$ is a Banach space with the UMD property. This gives a new proof and an extension of a classical result of Besov-Il'in-Nikol'skiĭ for scalar functions.
Publié le : 2007-07-15
Classification:  46E35,  46E40 
@article{1258131100,
     author = {Hyt\"onen, Tuomas P.},
     title = {Estimates for partial derivatives of vector-valued functions},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 731-742},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258131100}
}

Hytönen, Tuomas P. Estimates for partial derivatives of vector-valued functions. Illinois J. Math., Tome 51 (2007) no. 3, pp.  731-742. http://gdmltest.u-ga.fr/item/1258131100/