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References
- Albiac, Fernando; Kalton, Nigel J. Topics in Banach space theory. Graduate Texts in Mathematics, 233. Springer, New York, 2006. xii+373 pp. ISBN: 978-0387-28141-4; 0-387-28141-X MR2192298
- Aronszajn, N.; Gagliardo, E. Interpolation spaces and interpolation methods. Ann. Mat. Pura Appl. (4) 68 1965 51--117. MR0226361
- Bourgain, Jean. Vector-valued singular integrals and the $H^ 1$-BMO duality. Probability theory and harmonic analysis (Cleveland, Ohio, 1983), 1--19, Monogr. Textbooks Pure Appl. Math., 98, Dekker, New York, 1986. MR0830227
- Brzeźniak, Zdzisław; Hausenblas, Erika. Maximal regularity for stochastic convolutions driven by Lévy processes. Probab. Theory Related Fields 145 (2009), no. 3-4, 615--637. MR2529441
- Burkholder, D. L. Distribution function inequalities for martingales. Ann. Probability 1 (1973), 19--42. MR0365692
- Burkholder, D. L. A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Ann. Probab. 9 (1981), no. 6, 997--1011. MR0632972
- Burkholder, Donald L. Martingales and singular integrals in Banach spaces. Handbook of the geometry of Banach spaces, Vol. I, 233--269, North-Holland, Amsterdam, 2001. MR1863694
- Carlen, Eric A.; Pardoux, Étienne. Differential calculus and integration by parts on Poisson space. Stochastics, algebra and analysis in classical and quantum dynamics (Marseille, 1988), 63--73, Math. Appl., 59, Kluwer Acad. Publ., Dordrecht, 1990. MR1052702
- Çınlar, Erhan. Probability and stochastics. Graduate Texts in Mathematics, 261. Springer, New York, 2011. xiv+557 pp. ISBN: 978-0-387-87858-4 MR2767184
- Clément, P.; de Pagter, B.; Sukochev, F. A.; Witvliet, H. Schauder decomposition and multiplier theorems. Studia Math. 138 (2000), no. 2, 135--163. MR1749077
- Dermoune, A.; Krée, P.; Wu, L. Calcul stochastique non adapté par rapport à la mesure aléatoire de Poisson. (French) [Nonadapted stochastic calculus with respect to the Poisson random measure] Séminaire de Probabilités, XXII, 477--484, Lecture Notes in Math., 1321, Springer, Berlin, 1988. MR0960543
- G. Di Nunno, B. Oksendal, and F. Proske, phMalliavin calculus for Lévy processes with applications to finance, Universitext, Springer-Verlag, Berlin, 2009. MR2460554 (2010f:60001)
- S. Dirksen, phItô isomorphisms for L^p-valued Poisson stochastic integrals, Arxiv 1208.3885.
- Fendler, Gero. Dilations of one parameter semigroups of positive contractions on $L^ p$ spaces. Canad. J. Math. 49 (1997), no. 4, 736--748. MR1471054
- Fröhlich, Andreas M.; Weis, Lutz. $H^ \infty$ calculus and dilations. Bull. Soc. Math. France 134 (2006), no. 4, 487--508. MR2364942
- Hausenblas, Erika. Maximal inequalities of the Itô integral with respect to Poisson random measures or Lévy processes on Banach spaces. Potential Anal. 35 (2011), no. 3, 223--251. MR2832576
- Hausenblas, Erika; Seidler, Jan. A note on maximal inequality for stochastic convolutions. Czechoslovak Math. J. 51(126) (2001), no. 4, 785--790. MR1864042
- Junge, Marius; Xu, Quanhua. Noncommutative Burkholder/Rosenthal inequalities. Ann. Probab. 31 (2003), no. 2, 948--995. MR1964955
- Kabanov, Ju. M. Extended stochastic integrals. (Russian) Teor. Verojatnost. i Primenen. 20 (1975), no. 4, 725--737. MR0397877
- Kunita, Hiroshi. Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms. Real and stochastic analysis, 305--373, Trends Math., Birkhäuser Boston, Boston, MA, 2004. MR2090755
- Last, Günter; Penrose, Mathew D. Martingale representation for Poisson processes with applications to minimal variance hedging. Stochastic Process. Appl. 121 (2011), no. 7, 1588--1606. MR2802467
- Last, Günter; Penrose, Mathew D. Poisson process Fock space representation, chaos expansion and covariance inequalities. Probab. Theory Related Fields 150 (2011), no. 3-4, 663--690. MR2824870
- Ledoux, Michel; Talagrand, Michel. Probability in Banach spaces. Isoperimetry and processes. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 23. Springer-Verlag, Berlin, 1991. xii+480 pp. ISBN: 3-540-52013-9 MR1102015
- Løkka, Arne. Martingale representation of functionals of Lévy processes. Stochastic Anal. Appl. 22 (2004), no. 4, 867--892. MR2062949
- Maas, Jan. Malliavin calculus and decoupling inequalities in Banach spaces. J. Math. Anal. Appl. 363 (2010), no. 2, 383--398. MR2564861
- Maas, Jan; van Neerven, Jan. A Clark-Ocone formula in UMD Banach spaces. Electron. Commun. Probab. 13 (2008), 151--164. MR2399277
- Marinelli, Carlo; Prévôt, Claudia; Röckner, Michael. Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise. J. Funct. Anal. 258 (2010), no. 2, 616--649. MR2557949
- Marinelli, Carlo; Röckner, Michael. Well-posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise. Electron. J. Probab. 15 (2010), no. 49, 1528--1555. MR2727320
- Maurey, B. Système de Haar. (French) Séminaire Maurey-Schwartz 1974–1975: Espaces L$\sup{p}$, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. I et II, 26 pp. (erratum, p. 1) Centre Math., École Polytech., Paris, 1975. MR0420839
- J.M.A.M. van Neerven, phStochastic evolutions equations, 2007, Lecture notes of the 2007 Internet Seminar, available at repository.tudelft.nl.
- van Neerven, J. M. A. M.; Veraar, M. C.; Weis, L. Stochastic integration in UMD Banach spaces. Ann. Probab. 35 (2007), no. 4, 1438--1478. MR2330977
- Nualart, David. The Malliavin calculus and related topics. Second edition. Probability and its Applications (New York). Springer-Verlag, Berlin, 2006. xiv+382 pp. ISBN: 978-3-540-28328-7; 3-540-28328-5 MR2200233
- Nualart, David; Vives, Josep. Anticipative calculus for the Poisson process based on the Fock space. Séminaire de Probabilités, XXIV, 1988/89, 154--165, Lecture Notes in Math., 1426, Springer, Berlin, 1990. MR1071538
- Pisier, Gilles. Martingales with values in uniformly convex spaces. Israel J. Math. 20 (1975), no. 3-4, 326--350. MR0394135
- Privault, Nicolas. Chaotic and variational calculus in discrete and continuous time for the Poisson process. Stochastics Stochastics Rep. 51 (1994), no. 1-2, 83--109. MR1380764
- Rosiński, J. Random integrals of Banach space valued functions. Studia Math. 78 (1984), no. 1, 15--38. MR0766703
- J.L. Rubio de Francia, phMartingale and integral transforms of Banach space valued functions, Probability and Banach spaces (Zaragoza, 1985), Lecture Notes in Math., vol. 1221, Springer, Berlin, 1986, pp. 195--222. MRMR875011 (88g:42020)
- Rüdiger, B. Stochastic integration with respect to compensated Poisson random measures on separable Banach spaces. Stoch. Stoch. Rep. 76 (2004), no. 3, 213--242. MR2072381
- Stein, Elias M. Topics in harmonic analysis related to the Littlewood-Paley theory. Annals of Mathematics Studies, No. 63 Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo 1970 viii+146 pp. MR0252961
- M. Veraar, Stochastic integration in Banach spaces and applications to parabolic evolution equations, Ph.D. thesis, Delft University of Technology, 2006.
- Wu, Liming. A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields 118 (2000), no. 3, 427--438. MR1800540
- J. Zhu, Maximal inequalities for stochastic convolutions driven by Lévy processes in Banach spaces, Work in progress.

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