$$\end{document} In the following, the Banach space which is continuously embedded in the space of continuous functions , will be the solution space, and a nonvoid closed convex set K⊂ X shall capture the imposed boundary conditions.
Since the space (W_{0}^{1,2}(mathbb{R}_,mathbb{C}^{m})) is continuously embedded into (C( mathbb{R}_,mathbb{C}^{m})), the Banach space of bounded continuous functions on (mathbb{R}_).
It is easy to check that W ( 0, T ; V ) is continuously embedded into C ( 0, T ; H ) which denotes the space of continuous functions.
HereHdenotes a Hilbert space densely and continuously embedded inE.
Thus any space which can be continuously embedded in, can be also embedded in, where.
If (k>0), the space (mathbf{D}_{k}) is continuously embedded in AC.
The space (mathbf{D}_{k}) is continuously embedded into AC by Lemma 3.
By Hölder inequality, the space is continuously embedded into the dual space.
Suppose (L t)) satisfies (L ′, then (X^{alpha}) is continuously embedded in (H^{alpha}).
Note that E is continuously embedded in L p ( R, R N ) for all p ∈ [ 2, + ∞ ].
(X hookrightarrow Y) means that X is continuously embedded in Y.
