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On Interpolation of Compact Nonlinear Operators

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1990
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Cambridge Univ. Press
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We prove that the classical Lions-Peetre compactness theorems for linear operators still hold for Lipschitz operators. As a consequence, we deduce that certain Uryson integral operators are compact. We also show that Lipschitz operators can be interpolated by a wide class of J-functors.
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Análisis funcional y teoría de operadores
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J. BERGH and J. LOFSTROM, Interpolation spaces: an introduction (Springer, Berlin, 1976). F. COBOS, 'Interpolation of compact operators by Goulaouic procedure', Studia Math., to appear. F. COBOS, D. E. EDMUNDS and A. J. B. POTTER, 'Real interpolation and compact linear operators', J. Fund. Anal., to appear. F. COBOS and D. L. FERNANDEZ, 'On interpolation of compact operators', Ark. Mat. 27 (1989) 211-217. F. COBOS and J. PEETRE, 'Interpolation of compactness using Aronszajn-Gagliardo functors', Israel J. Math., to appear. M. CWIKEL, 'Real and complex interpolation and extrapolation of compact operators', preprint. M. A. KRASNOSELSKII, 'On a theorem of M. Riesz', Soviet Math. Dokl. 1 (1960) 229-231. M. A. KRASNOSELSKII, P. P. ZABREIKO, E. I. PUSTYLNIK and P. E. SBOLEVSKII, Integral operators in spaces of summable functions (Noordhoff, Leyden, 1976). J. L. LIONS and J. PEETRE, 'Sur une classe d'espaces d'interpolation', IHES Publ. Math. 19 (1964) 5-68. A. MANES and M. P. POLETTI, 'Qualche risultato sull'interpolazione per applicazioni non lineari fra spazi di Banach', Rend. Sent. Mat. Univ. Padova 47 (1972) 115-128. P. NILSSON, 'Reiteration theorems for real interpolation and approximation spaces', Ann. Mat. Pura Appl. 32 (1982) 291-330. J. PEETRE, 'A theory of interpolation of normed spaces', Lecture notes, Brasilia, 1963 [Notas de Matematica 39 (1968) 1-86]. J. PEETRE, 'Interpolation of Lipschitz operators and metric spaces', Mathematica 12 (35) (1970) 325-334. A. PERSSON, 'Compact linear mappings between interpolation spaces', Ark. Mat. 5 (1964) 215-219. L. TARTAR, 'Interpolation non lineaire et regularite', J. Fund. Anal. 9 (1972) 469-489. H. TRIEBEL, Interpolation theory, function spaces, differential operators (North-Holland, Amsterdam, 1978).
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https://hdl.handle.net/20.500.14352/57283
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