Reiteration theorems for the interpolation of quasi-subadditive functions on Banach spaces
Ralph Chill
Institut für Analysis, Fakultäat Mathematik, Technische Universität Dresden, Dresden, Germany
Search for more papers by this authorPraveen Sharma
Department of Mathematics, University of Delhi, Delhi, India
Shri Vishwakarma Skill University, Dudhola, Palwal, Haryana, India
Search for more papers by this authorCorresponding Author
Sachi Srivastava
Department of Mathematics, University of Delhi, Delhi, India
Correspondence
Sachi Srivastava, Department of Mathematics, University of Delhi, 110007, Delhi, India.
Email: [email protected]
Search for more papers by this authorRalph Chill
Institut für Analysis, Fakultäat Mathematik, Technische Universität Dresden, Dresden, Germany
Search for more papers by this authorPraveen Sharma
Department of Mathematics, University of Delhi, Delhi, India
Shri Vishwakarma Skill University, Dudhola, Palwal, Haryana, India
Search for more papers by this authorCorresponding Author
Sachi Srivastava
Department of Mathematics, University of Delhi, Delhi, India
Correspondence
Sachi Srivastava, Department of Mathematics, University of Delhi, 110007, Delhi, India.
Email: [email protected]
Search for more papers by this authorAbstract
We study reiteration theorems for quasi-subadditive functions on Banach spaces. We prove various reiteration theorems that are generalizations of classical reiteration theorems.
REFERENCES
- 1V. Barbu, Nonlinear differential equations of monotone types in Banach spaces, Springer Monographs in Mathematics, Springer, New York, 2010.
- 2C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Boston, MA, 1988.
- 3J. Bergh and J. Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, vol. 223, Springer-Verlag, Berlin 1976.
10.1007/978-3-642-66451-9 Google Scholar
- 4J. Beurich, Euler schemes for accretive operators on Banach spaces, Ph.D. thesis, TU Dresden, Dresden, 2023.
- 5J. Beurich and P. Sharma, Interpolation results for convergence of implicit Euler schemes with accretive operators, Nonlinear Differ. Equ. Appl. 31 (2024), no. 6, 109.
- 6D. Brézis, Interpolation et opérateurs non linéaires, Thèse de doctorat, Université Paris VI, 1974.
- 7D. Brézis, Perturbations singulières et problèmes d'évolution avec défaut d'ajustement, C. R. Acad. Sci. Paris Sér. A-B. 276 (1973), A1597–A1600.
- 8H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North Holland Mathematics Studies, vol. 5, North-Holland, Amsterdam, 1973.
- 9R. Chill, P. Sharma, and S. Srivastava, Real interpolation of functions with applications to accretive operators on Banach spaces, J. Differ. Equ. 402 (2024), 554–592.
- 10A. Dufetel, Interpolation non-linéaire associée à un opérateur -accretif dans un espace de Banach, Thèse de doctorat, Université de Franche-Comté, Besançon, 1981.
- 11A. Dufetel, Interpolation non linéaire dans un espace de Banach, C. R. Acad. Sci. Paris Sér. I Math. 293, no. 6, 331–334.
- 12A. Lunardi, Interpolation theory, 2nd ed., Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) [Lecture Notes. Scuola Normale Superiore di Pisa (New Series)], Edizioni della Normale, Pisa, 2009.
- 13A. Lunardi, Analytic semigroups and optimal regularity in parabolic problems, Progress in Nonlinear Differential Equations and Their Applications, vol. 16, Birkhäuser, Basel, 1995.
- 14V. Maz'ya, Sobolev spaces with applications to elliptic partial differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 342, Springer, Heidelberg, augmented edition, 2011.
10.1007/978-3-642-15564-2 Google Scholar
- 15J. Peetre, A new approach in interpolation spaces, Studia Math. 34 (1970), 23–42.
- 16J. Peetre, G. Sparr, Interpolation of normed abelian groups, Ann. Mat. Pura Appl. 92 (1972), no. 4, 217–262.
10.1007/BF02417949 Google Scholar
- 17L. Tartar, Interpolation non linéaire et régularité, J. Funct. Anal. 9 (1972), 469–489.
10.1016/0022-1236(72)90022-5 Google Scholar
- 18L. Tartar, Interpolation non linéaire, Actes du Colloque d'Analyse Fonctionnelle (Univ. de Bordeaux, Bordeaux, 1971), Bull. Soc. Math. France, Mém. No. 31–32. Soc. Math. France, Paris, 1972, pp. 375–380.
- 19H. Triebel, Interpolation theory, function spaces, differential operators, 2nd ed., Johann Ambrosius Barth, Heidelberg, 1995.
