Asymptotic sharpness of a Bernstein-type inequality for rational functions in H^{2}

A Bernstein-type inequality in the standard Hardy space H^{2} of the unit disc \mathbb{D}=\{z\in\mathbb{C}:\,|z|<1\}, for rational functions in \mathbb{D} having at most n poles all outside of \frac{1}{r}\mathbb{D},

R-boundedness Approach to linear third differential equations in a UMD Space

The aim of this work is to study the existence of a periodic solutions of third order differential equations $z'''(t) = Az(t) + f(t)$ with the periodic condition $x(0) = x(2\pi), x'(0) = x'(2\pi)$ and $x''(0) = x''(2\pi)$. Our approach is based on the R-boundedness and $L^{p}$-multiplier of linear operators

Application of a Bernstein type inequality to rational interpolation in the Dirichlet space

We prove a Bernstein-type inequality involving the Bergman and the Hardy norms, for rational functions in the unit disc \mathbb{D} having at most n poles all outside of \frac{1}{r}\mathbb{D}, 0Comment: Journal of Mathematical Sciences (New York) \`a para\^itre, \`a para\^itre (2011) \`a para\^itr

Periodic solutions of integro-differential equations in Banach space having Fourier type

The aim of this work is to study the existence of a periodic solutions of integro-differential equations d dt [x(t)-- L(x t)] = A[x(t)-- L(x t)]+ G(x t)+ t --$\infty$ a(t-- s)x(s)ds+ f (t), (0 $\le$ t $\le$ 2$\pi$) with the periodic condition x(0) = x(2$\pi$), where a $\in$ L 1 (R +). Our approach is based on the M-boundedness of linear operators, Fourier type, B s p,q-multipliers and Besov spaces.Comment: arXiv admin note: text overlap with arXiv:1707.0787