TEUBNER-TEXTE zur Mathematik Band 133. H.-J. Schmeisser I H. Triebe! (Hrsg.) Function Spaces, Differential Operators and Nonlinear Analysis

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1 TEUBNER-TEXTE zur Mathematik Band 133 H.-J. Schmeisser I H. Triebe! (Hrsg.) Function Spaces, Differential Operators and Nonlinear Analysis

2 TEUBNER-TEXTE zur Mathematik Herausgegeben von Prof. Dr. Jochen Brüning, Augsburg Prof. Dr. Herbert Gajewski, Berlin Prof. Dr. Herbert Kurke, Berlin Prof. Dr. Hans Triebe!, Jena Die Reihe soll ein Forum für Beiträge zu aktuellen Problemstellungen der Mathematik sein. Besonderes Anliegen ist die Veröffentlichung von Darstellungen unterschiedlicher methodischer Ansätze, die das Wechselspiel zwischen Theorie und Anwendungen sowie zwischen Lehre und Forschung reflektieren. Thematische Schwerpunkte sind Analysis, Geometrie und Algebra. ln den Texten sollen sich sowohl Lebendigkeit und Originalität von Spezialvorlesungen und Seminaren als auch Diskussionsergebnisse aus Arbeitsgruppen widerspiegeln. TEUBNER-TEXTE erscheinen in deutscher oder englischer Sprache.

3 Function Spaces, Differential Operators and Nonlinear Analysis Edited by Prof. Dr. Hans-Jürgen Schmeisser Prof. Dr. Hans Triebe! Friedrich-Schiller-University, Jena Springer Fachmedien Wiesbaden GmbH 1993

4 Prof. Dr. Hans-Jurgen Schmelsser Born in 1950 in Trusetal (Thuringia). Studied mathematics in Jena from 1968 to 1973 and in Moscow from 1979 to Received Dr. rer. nat. in 1978 and Dr. sc. nat. in 1982 from the Friedrich-Schiller-University of Jena. Since 1992 Professor of Analysis at the University of Jena. Fields of interest: Fourier analysis and function spaces. Prof. Dr. Hans Trlebel Born in 1936 in Dessau. Studied mathematics in Jena from 1954 to 1959 and in Leningrad (St. Petersburg) from 1963 to Received Dr. rer. nat. in 1962 and Dr. habil in 1966 from the Friedrich-Schiller-University of Jena. Since 1970 Professor of Analysis at the University of Jena. Fields of interest: Function spaces of partial differential equations. Die Deutsche Bibliothek - CIP-Einheitsaufnahme Function spaces, differential operators and nonlinear analysis I ed. by Hans-JOrgen Schmeisser ; Hans Triebel. - (Teubner-Texte zur Mathematik ; 133) ISBN ISBN (ebook) DOI / NE: Schmeisser, Hans-JOrgen [Hrsg.); GT Das Werk einschliebiich aller seiner Teile ist urheberrechtlich geschotzt. Jede Verwertung auber halb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlages unzulassig und stralbar. Das gilt besonders for VervielfiUtigungen, Obersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Springer Fachmedien Wiesbaden 1993 Ursprünglich erschienen bei B. G. Teubner Verlagsgesellschaft Leipzig 1993 Umschlaggestaltung: E. Kretschmer, Leipzig

5 Preface The present Teubner-Text contains invited surveys and shorter communications connected with the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis", which took place in Friedrichroda (Thuringia, Germany) from September 20-26, The main subjects are weil reflected by the table of contents. 55 mathematicians attended the conference, many of them from eastern countries. We take the opportunity to thank DFG for financial support, which enabled us to invite mathematicians from the former socialist countries, and especially from the former Soviet Union, and which gave us the possibility to maintain and to strengthen our contacts to these centers of the theory of function spaces and its application to PDE's, \li'de's and approximation theory. The organization of the conference as weil as the final preparation of this text was mostly done by our co-workers in Jena. We wish to thank all of them for the generaus support they gave us far beyond their duties (whatever this means in connection with the organization of a conference). The final preparation of this text was mainly done by Dr. M. Malarski. Furthermore Dr. M. Geisler, Ms. D. Haroske and Dr. W. Sicke! converted some manuscript in readable papers on TEX-standard Ievel. We wish to thank them for doing this time-consuming work. Jena, May 13, 1993 H.-J. Schmeisser H. Triebe!

6 Contents I Survey Articles 9 Herbert Amann Nonhomogeneaus Linear and Quasilinear Elliptic and Parabolic Boundary Value Problems Gerard Bourdaud The Functional Calculus in Sobolev Spaces Pavel Drabek Solvability of Strongly Nonlinear Degenerated Elliptic Problems M. Krbec, B. Opic, L. Pick, J. Rakosnik Some Recent Results on Hardy Type Operators in Weighted Function Spaces and Related Topics P. I. Lizorkin, Sergej M. Nikolskii Approximations of Functions on Manifolds Stanislav I. Pohozaev The Sharp Apriori Estimates for Some Superlinear Degenerate Elliptic Problems Thomas Runst Singularity Theory in Function Spaces Abdellah Youssfi Function Spaces Related to Singular Integral Operators II Communications Viktor I. Burenkov Conditional Hypoellipticity and Fourier Multipliers for Weighted Lp-Spaces with an Exponential Weight Ioseb Genebashvili, Amirau Gogatishvili, Vakhtang Kokilashvili Salutions of Some Weight Problems

7 8 Michael L. Gol'dman On Integral Inequalities on the Set of Functions with Some Properties of Monotonicity 274 Niels Jacob Anisotropie Sobolev Spaces in Probability Theory Alf Jonsson Atomic Decomposition of Besov Spaces on Closed Sets Alois K ufner Some Remarks Concerning the Hardy Inequality Tarnara Tararykova Inequalities for Integral and Discrete Norms of Entire Functions of Exponential Type 295 List of Participants