Estimates for vector valued Dirichlet polynomials

[EN] We estimate the -norm of finite Dirichlet polynomials with coefficients in a Banach space. Our estimates quantify several recent results on Bohr's strips of uniform but non absolute convergence of Dirichlet series in Banach spaces.A. Defant and P. Sevilla-Peris were supported by MICINN Project MTM2011-22417.Defant, A.; Schwarting, U.; Sevilla Peris, P. (2014). Estimates for vector valued Dirichlet polynomials. Monatshefte f�r Mathematik. 175(1):89-116. https://doi.org/10.1007/s00605-013-0600-4S891161751Balasubramanian, R., Calado, B., Queffélec, H.: The Bohr inequality for ordinary Dirichlet series. Studia Math. 175(3), 285–304 (2006)Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Monatsh. Math. 136(3), 203–236 (2002)Bennett, G.: Inclusion mappings between $$l^{p}$$ l p spaces. J. Funct. Anal. 13, 20–27 (1973)Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann. Math. (2) 32(3), 600–622 (1931)Bohr, H.: Über die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichlet–schen Reihen $$\sum \frac{a_n}{n^s}$$ ∑ a n n s . Nachr. Ges. Wiss. Göttingen Math. Phys. Kl., Heft 4, 441–488 (1913)Bohr, H.: Über die gleichmäßige Konvergenz Dirichletscher Reihen. J. Reine Angew. Math. 143, 203–211 (1913)Carl, B.: Absolut- $$(p,\,1)$$ ( p , 1 ) -summierende identische Operatoren von $$l_{u}$$ l u in $$l_{v}$$ l v . Math. Nachr. 63, 353–360 (1974)Carlson, F.: Contributions à la théorie des séries de Dirichlet. Note i. Ark. fö”r Mat., Astron. och Fys. 16(18), 1–19 (1922)de la Bretèche, R.: Sur l’ordre de grandeur des polynômes de Dirichlet. Acta Arith. 134(2), 141–148 (2008)Defant, A., Frerick, L., Ortega-Cerdà, J., Ounaïes, M., Seip, K.: The Bohnenblust–Hille inequality for homogeneous polynomials is hypercontractive. Ann. Math. (2) 174(1), 485–497 (2011)Defant, A., García, D., Maestre, M., Pérez-García, D.: Bohr’s strip for vector valued Dirichlet series. Math. Ann. 342(3), 533–555 (2008)Defant, A., García, D., Maestre, M., Sevilla-Peris, P.: Bohr’s strips for Dirichlet series in Banach spaces. Funct. Approx. Comment. Math. 44(part 2), 165–189 (2011)Defant, A., Maestre, M., Schwarting, U.: Bohr radii of vector valued holomorphic functions. Adv. Math. 231(5), 2837–2857 (2012)Defant, A., Popa, D., Schwarting, U.: Coordinatewise multiple summing operators in Banach spaces. J. Funct. Anal. 259(1), 220–242 (2010)Defant, A., Sevilla-Peris, P.: Convergence of Dirichlet polynomials in Banach spaces. Trans. Am. Math. Soc. 363(2), 681–697 (2011)Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge Studies in Advanced Mathematics, vol. 43. Cambridge University Press, Cambridge (1995)Harris, L.A.: Bounds on the derivatives of holomorphic functions of vectors. In: Analyse fonctionnelle et applications (Comptes Rendus Colloq. Analyse, Inst. Mat., Univ. Federal Rio de Janeiro, Rio de Janeiro, 1972), pp. 145–163. Actualités Aci. Indust., No. 1367. Hermann, Paris (1975)Hedenmalm, H., Lindqvist, P., Seip, K.: A Hilbert space of Dirichlet series and systems of dilated functions in $$L^2(0,1)$$ L 2 ( 0 , 1 ) . Duke Math. J. 86(1), 1–37 (1997)Kahane, J.-P.: Some Random Series of Functions. Cambridge Studies in Advanced Mathematics, vol. 5, 2nd edn. Cambridge University Press, Cambridge (1985)Konyagin, S.V., Queffélec, H.: The translation $$\frac{1}{2}$$ 1 2 in the theory of Dirichlet series. Real Anal. Exch. 27(1):155–175 (2001/2002)Kwapień, S.: Some remarks on $$(p,\, q)$$ ( p , q ) -absolutely summing operators in $$l_{p}$$ l p -spaces. Studia Math. 29, 327–337 (1968)Ledoux, M., Talagrand, M.: Probability in Banach Spaces: Isoperimetry and Processes, reprint of the 1991 edn. Classics in Mathematics. Springer, Berlin (2011)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. I. Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 92. Springer, Berlin (1977)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. II, Function Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97. Springer, Berlin (1979)Maurizi, B., Queffélec, H.: Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl. 16, 676–692 (2010)Prachar, K.: Primzahlverteilung. Springer, Berlin (1957)Queffélec, H.: H. Bohr’s vision of ordinary Dirichlet series; old and new results. J. Anal. 3, 43–60 (1995)Tomczak-Jaegermann, N.: Banach–Mazur Distances and Finite-Dimensional Operator Ideals. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38. Longman Scientific & Technical, Harlow (1989

Clinical outcomes and safety of rituximab treatment for patients with systemic lupus erythematosus (SLE) - results from a nationwide cohort in Germany (GRAID)

ObjectiveThe objective of this article is to evaluate the safety and clinical outcome of rituximab treatment in systemic lupus erythematosus (SLE) patients refractory to standard of care therapy in a real-life setting in Germany. MethodsThe GRAID registry included patients with different autoimmune diseases who were given off-label treatment with rituximab. Data on safety and clinical response were collected retrospectively. In SLE patients, clinical parameters included tender and swollen joint counts, fatigue, myalgia, general wellbeing, Raynaud's and the SLEDAI index. Laboratory tests included dsDNA antibody titres, complement factors, hematologic parameters and proteinuria. Finally, the investigators rated their patients as non-, partial or complete responders based on clinical grounds. ResultsData from 85 SLE patients were collected, 69 female and 16 male, with a mean disease duration of 9.8 years. The mean follow-up period was 9.67.4 months, resulting in 66.8 patient years of observation. A complete response was reported in 37 patients (46.8%), partial response in 27 (34.2%), no response in 15 (19.0%). On average, major clinical as well as laboratory efficacy parameters improved substantially, with the SLEDAI decreasing significantly from 12.2 to 3.3 points. Concerning safety, one infusion reaction leading to discontinuation of treatment occurred. Infections were reported with a rate of 19.5 (including six severe infections) per 100 patient years. ConclusionWith the restrictions of a retrospective data collection, the results of this study confirm data of other registries, which suggest a favourable benefit-risk ratio of rituximab in patients with treatment-refractory SLE

Bidirectional regulation of bone formation by exogenous and osteosarcoma-derived Sema3A

Semaphorin 3A (Sema3A), a secreted member of the Semaphorin family, increases osteoblast differentiation, stimulates bone formation and enhances fracture healing. Here, we report a previously unknown role of Sema3A in the regulation of ectopic bone formation and osteolysis related to osteosarcoma. Human recombinant (exogenous) Sema3A promoted the expression of osteoblastic phenotype in a panel of human osteosarcoma cell lines and inhibited the ability of these cells to migrate and enhance osteoclastogenesis in vitro. In vivo, administration of exogenous Sema3A in mice after paratibial inoculation of KHOS cells increased bone volume in non-inoculated and tumour-bearing legs. In contrast, Sema3A overexpression reduced the ability of KHOS cells to cause ectopic bone formation in mice and to increase bone nodule formation by engaging DKK1/β-catenin signalling. Thus, Sema3A is of potential therapeutic efficacy in osteosarcoma. However, inhibition of bone formation associated with continuous exposure to Sema3A may limit its long-term usefulness as therapeutic agent

Clinical outcomes and safety of rituximab treatment for patients with systemic lupus erythematosus (SLE) - results from a nationwide cohort in Germany (GRAID)

ObjectiveThe objective of this article is to evaluate the safety and clinical outcome of rituximab treatment in systemic lupus erythematosus (SLE) patients refractory to standard of care therapy in a real-life setting in Germany. MethodsThe GRAID registry included patients with different autoimmune diseases who were given off-label treatment with rituximab. Data on safety and clinical response were collected retrospectively. In SLE patients, clinical parameters included tender and swollen joint counts, fatigue, myalgia, general wellbeing, Raynaud's and the SLEDAI index. Laboratory tests included dsDNA antibody titres, complement factors, hematologic parameters and proteinuria. Finally, the investigators rated their patients as non-, partial or complete responders based on clinical grounds. ResultsData from 85 SLE patients were collected, 69 female and 16 male, with a mean disease duration of 9.8 years. The mean follow-up period was 9.67.4 months, resulting in 66.8 patient years of observation. A complete response was reported in 37 patients (46.8%), partial response in 27 (34.2%), no response in 15 (19.0%). On average, major clinical as well as laboratory efficacy parameters improved substantially, with the SLEDAI decreasing significantly from 12.2 to 3.3 points. Concerning safety, one infusion reaction leading to discontinuation of treatment occurred. Infections were reported with a rate of 19.5 (including six severe infections) per 100 patient years. ConclusionWith the restrictions of a retrospective data collection, the results of this study confirm data of other registries, which suggest a favourable benefit-risk ratio of rituximab in patients with treatment-refractory SLE

Mild Sensory Stimulation Completely Protects the Adult Rodent Cortex from Ischemic Stroke

Despite progress in reducing ischemic stroke damage, complete protection remains elusive. Here we demonstrate that, after permanent occlusion of a major cortical artery (middle cerebral artery; MCA), single whisker stimulation can induce complete protection of the adult rat cortex, but only if administered within a critical time window. Animals that receive early treatment are histologically and behaviorally equivalent to healthy controls and have normal neuronal function. Protection of the cortex clearly requires reperfusion to the ischemic area despite permanent occlusion. Using blood flow imaging and other techniques we found evidence of reversed blood flow into MCA branches from an alternate arterial source via collateral vessels (inter-arterial connections), a potential mechanism for reperfusion. These findings suggest that the cortex is capable of extensive blood flow reorganization and more importantly that mild sensory stimulation can provide complete protection from impending stroke given early intervention. Such non-invasive, non-pharmacological intervention has clear translational potential