Complex convexity

Abstract: A note on the Ishihara and Takahashi modulus of convexity J. Alonso and A. Ullan 1. A property of non-strongly regular operators S. Agyros and M. Petrakis 2. The entropy of convex bodies with 'few' extreme points K. Ball and A. Pajor 3. Spaces of vector-valued analytic functions and applications P. G. Casazza and N. J. Kalton 4. Moduli of complex convexity W. Davis 5. Grothendieck-type inequalities and weak Hilbert spaces M. Defant and M. Junge 6. A weak topology characterization of l1(m) S. J. Dilworth 7. Singular integral operators: a martingale approach T. Figiel 8. Remarks about the interpolation of Radon-Nikodym operators N. Ghoussoub, B. Maurey and W. Schachermayer 9. Symmetric sequences in finite-dimensional normed spaces T. Gowers 10. Some topologies on the space of analytic self-maps of the unit disk H. Hunziker, H. Jarchow and V. Mascioni 11. Minimal and strongly minimal Orlicz spaces N. J. Kalton 12. Type and cotype in Musielak-Orlicz spaces A. Kaminska and B. Turett 13. On the complex Grothendieck constant in the n-dimensional case H. Konig 14. Pathological properties and dichotomies for random quotients of finite-dimensional Banach spaces P. Mankiewicz and N. Tomczak-Jaegermann 15. A note on a low M*-estimate V. Milman 16. The p1/p in Pisier's factorization theorem S. J. Montgomery-Smith 17. When E and E[E] are isomorphic C. J. Read 18. A note on Gaussian measure of translates of balls M. Talagrand 19. Sublattices of M(X) isometric to M[0,1] L. W. Weiss.

Abstract: Let 2 p 0s uch thatfHp(X) (� f(0)� p + λ (1 −| z| 2 ) p−1 � f � (z)� p dA(z)) 1/p ,f or all f ∈ H p (X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided.

Abstract: We prove a complex version of Kostant's non-linear convexity theorem. Applications to the construction of G-invariant Grauert tubes of non-compact Riemannian symmetric G/K spaces are given.