Abstract
It has become apparent that the concept of families ofR-boundedoperators plays an important role in operator theory, in the theory of operator-valued Fourier multipliers, and also in maximal regularity of elliptic and parabolic problems. Although this theory is only of recent origin, already a number of nontrivial applications have been appeared and we expect that in the near future there will be many more.
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J.B. Baillon and Ph. ClémentExamples of unbounded imaginary powers of operators.J. Funct. Anal. 100 (1991), 419–434.
Ph. Clément,B.de Pagter,F.A.Sukochev,and H. WitvlietSchauder decompositions and multiplier theorems. Studia Math. 138 (2000), 135–163. Preprint.
Ph. Clément and P. Egberts,On the sum of maximal monotone operators.Diff.Integral.Eqns. 3 (1990), 1127–1138.
Ph. Clément and J. PrüssCompletely positive measures and Feller semigroups.Math. Ann. 287 (1990), 73–105.
Ph.Clément and J. PrüssAn operator - valued transference principle and maximal regularity on vector - valued L 0 - spaces .In Evolution Equ. and Appl. Physical Life Sci., Lect. Notes Pure and Applied Math. 215, 17–26, Marcel Dekker, New York, 2001.
G. DaPrato and P. GrisvardSommes d’opérateurs linéaires et équations différentielles opérationelles.J. Math. Pures Appl. 54 (1975), 305–387.
W. Desch, M. Hieber, and J. Prüss,L0-theory of the Stokes equation in a half space. J. Evolution Eqns. 1 (2001).
G. DoreLP-regularity for abstract differential equations.In H. Komatsu, ed., Functional Analysis and Related Topics, Lecture Notes in Mathematics 1540, Springer Verlag, Berlin, 1993.
J. Escher, J. Prüss, and G. Simonett, Analytic solutions of the Stefan problem with Gibbs-Thomson correction. To appear.
M. Hieber and J. PrüFunctional calculi for linear operators in vector-valued Lspaces via the transference principle.Adv. Diff. Eqns. 3 (1998), 847–872.
N. Kalton and G. Lancien, Asolution to the problem of LP -maximal regularity.Math. Z. 235 (2000), 559–568.
N. Kalton and L. Weis, The H°°-calculus and sums of closed operators. Preprint, 2000.
H. KomatsuFractional powers of operators VI. Interpolation of non-negative operators and imbedding theorems.J. Fac. Sci. Univ. Tokyo, Sec. IA19(1972), 1–63.
A. McIntosh and A. Yagi Operators of type w without a bounded H°° functional calculus. In Miniconference on Operators in Analysis, Proc. Center Math. Analysis 24, Australian Nat. Univ., Canberra, 1989.
E. Stein, Topics in Harmonic Analysis related to the Littlewood-Paley Theory. Ann. Math. Studies 63, Princeton Univ. Press, Princeton, 1970.
L. WeisA new approach to maximal LP-regularity. In Evolution Equ. and Appl. Physical Life Sci., Lect. Notes Pure and Applied Math. 215, 195–214, Marcel Dekker, New York, 2001.
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Clément, P., Prüss, J. (2003). Some Remarks on Maximal Regularity of Parabolic Problems. In: Iannelli, M., Lumer, G. (eds) Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics. Progress in Nonlinear Differential Equations and Their Applications, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8085-5_7
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DOI: https://doi.org/10.1007/978-3-0348-8085-5_7
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