Том 71
№ 6

All Issues

Zontov V. A.

Articles: 1
Article (Russian)

Bernstein-type inequalities for splines defined on the real axis

Babenko V. F., Zontov V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 603-611

We obtain the exact inequalities of the Bernstein type for splines $s \in S_{m, h} \bigcap L_2 (\mathbb{R})$ as well as the exact inequalities that, for splines $s \in S_{m, h}, \quad h > 0$, estimate $L_p$-norms of the Fourier transforms of their $k$-th derivative by $L_p$-norms of the Fourier transforms of splines themselves.