Download Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March by Ali Baklouti, Aziz El Kacimi, Sadok Kallel, Nordine Mir PDF

By Ali Baklouti, Aziz El Kacimi, Sadok Kallel, Nordine Mir

This e-book comprises chosen papers awarded on the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) convention, held in reminiscence of Mohammed Salah Baouendi, a most famous determine within the box of a number of advanced variables, who kicked the bucket in 2011. All learn articles have been written through prime specialists, a few of whom are prize winners within the fields of advanced geometry, algebraic geometry and research. The publication deals a useful source for all researchers drawn to fresh advancements in research and geometry.

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Extra resources for Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi

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8 Let C be an annulus and B a ball of Rd centered at the origin. A constant C exists so that, for any nonnegative integer k, any couple ( p, q) in [1, ∞]2 with q ≥ p ≥ 1 and any function u of L p (Rd ), we have Supp u ⊂ λB =⇒ D k u L q (Rd ) := sup ∂ α u |α|=k Supp u ⊂ λC =⇒ C −k−1 λk u L p (Rd ) L q (Rd ) ≤ Dk u ≤ C k+1 λ L p (Rd ) k+d( 1p − q1 ) ≤ C k+1 λk u u L p (Rd ) L p (Rd ) . 3 Main Results The development of microlocal tools adapted to the framework of problems at hand is an important issue: we refer for instance to the articles [4, 8, 10, 16, 17] where was constructed respectively Littlewood-Paley decompositions on the Heisenberg group, on graded Lie groups and on Lie groups of polynomial growth satisfying properties as Bony’s decomposition ([13]) in the euclidean case, which enabled to transpose many classical results to these general settings.

Soc. 295, 347–368 (1986) 16. D. Grundmeier, J. Lebl, L. Vivas, Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics. Mathematische Annalen 358(3–4), 1059–1089 (2014) 17. X. Huang, On a linearity problem for proper maps between balls in complex spaces of different dimensions. J. Differ. Geom. 51(1), 13–33 (1999) 18. X. Huang, S. Ji, Mapping Bn into B2n−1 . Inventiones Mathematicae 145, 219–250 (2001) 19. S. Ji, Y. Zhang, Classification of rational holomorphic maps from B 2 into B N with degree 2.

A similar idea applies for hyperquadric maps. The key point is the following essentially trivial result. Given the set up in the proposition, we define a polynomial mapping from Cn−l × Cl to some C K × C L by E A,B ( f, g) = (π A f ⊗ z) ⊕ (π B g ⊗ w) ⊕ (1 − π A ) f, (π B g ⊗ z) ⊕ (π A f ⊗ w) ⊕ (1 − π B )g . 1 Let ( f, g) : Cn−l × Cl → C N1 × C N2 be a polynomial mapping whose components are linearly independent. Write (z, w) for the variables in the domain. Let A be a subspace of C N1 and let B be a subspace of C N2 .

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