Bernstein functions and rates in mean ergodic theorems for operator semigroupsJournal d'Analyse Mathematique - - 2012
Alexander Gomilko, Markus Haase, Yuri Tomilov
We present a functional calculus approach to the study of rates of decay in mean ergodic theorems for bounded strongly continuous operator semigroups. A central role is played by operators of the form g(A, where −A is the generator of the semigroup and g is a Bernstein function. In addition, we obtain some new results on Bernstein functions which are of independent interest.
Conformal invariants and higher-order schwarz lemmasJournal d'Analyse Mathematique - - 2003
Eric Schippers
We derive a generalization of the Grunsky inequalities using the Dirichlet principle. As a corollary, sharp distortion theorems for bounded univalent functions are proven for invariant differential expressions which are higher-order versions of the Schwarzian derivative. These distortion theorems can be written entirely in terms of conformai invariants depending on the derivatives of the hyperboli...... hiện toàn bộ
An extension of the Landau-Kolmogorov inequality. Solution of a problem of ErdösJournal d'Analyse Mathematique - Tập 78 - Trang 263-280 - 1999
Borislav Bojanov, Nikola Naidenov
For any fixed finite interval [a, b] on the real line, an arbitrary natural numberr and σ>0, we describe the extremal function to the problem
$$\left\| {f^{(k)} } \right\|L_p \left[ {a,b} \right]^{ \to \sup } \left( {1 \leqslant k \leqslant r - 1, 1 \leqslant p< \infty } \right)$$
over all function...... hiện toàn bộ
A reverse Denjoy theorem IIJournal d'Analyse Mathematique - Tập 110 - Trang 385-395 - 2010
P. C. Fenton, J. Rossi
For α satisfying 0 < α < π, suppose that C
1 and C
2 are rays from the origin, C
1: z = re
i(π−α) and C
2: z = re
i(π+α), r ≥ 0, and that D = {z: | arg z − π| < α}. Let u be a nonconstant subharmonic function in the plane and define B(r, u) = sup|z|=r
...... hiện toàn bộ