Sentence examples for bounded in the space from inspiring English sources

In particular, the bound is valid in (L^1) as well, which implies that (overline{E}^tau ) is bounded in the space of measures over ([0,T]times Omega ).

Therefore, it is bounded in the space.

Then c ≥ 0 and { ( u n, v n ) } is bounded in the space E. Proof.

It follows from Theorem 3.3 that u ε n x, ρ ε n x are bounded in the space L∞.

Proof Firstly, we will prove that the sequence { u n ( t, x ) } is uniformly bounded in the space H 1 ( [ 0, T ] × S ).

In order to show that is not dense in, we will construct a linear operator being bounded in the space but unbounded when restricted to.

It is shown that these transformations are bounded in the spaces LpγBn(Rn), p > 1, with a constant independent of the dimension an depending only on p and the number of different eigenvalues of the matrix B. The proof of this result is analytic and uses appropriate square-functions defined in terms of semigroups of operators related to LB and the Littlewood-Paley-Stein theory.

Now (p>1), and the set ({f_{n}, ngeq1}) is bounded in the reflexive space (L^{p}(Omega)), so it is relatively weakly compact in (L^{p}(Omega)).

Now (p>1), and the set ({g_{n}, ngeq1}) is bounded in the reflexive space (L^{p}(Omega)), so it is relatively weakly compact in (L^{p}(Omega)).

We assume that data are bounded in the feature space, that is, (left| phi left( xright) right| le R,;forall x,in mathcal {X}).

It asserts that given 02 and a Lipschitz domain Ω⊂C, the Beurling transform Bf="−p.v.1πz2⁎f is bounded in the Sobolev space Ws,p if and only if BχΩ∈Ws,p.