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Interpolation Spaces and Related Topics
Edited by: Michael Cwikel, Mario Milman, and Richard Rochberg
A publication of Bar-Ilan University.
Israel Mathematical Conference Proceedings
1992; 294 pp; softcover
Volume: 5
List Price: US$40
Member Price: US$32
Order Code: IMCP/5
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This book contains the proceedings of the International Workshop on Interpolation Spaces and Related Topics, held at Technion in Haifa, Israel, in the summer of 1990. Interpolation spaces have their roots in the classical interpolation theorems of Marcikiewicz and Riesz-Thorin. In the last three decades, the study of these spaces has developed into an extensive theory with applications in several fields, including harmonic analysis, partial differential equations, and geometry of Banach spaces. Substantial contributions have come from both sides of the former "Iron Curtain", and the Haifa Workshop was the first time that sizable contingents of experts from East and West could meet and interact.

The twenty-one research papers in this volume reflect recent developments at the frontier of research in several directions in interpolation theory. In addition, the volume provides a concise and convenient summary of interesting but hitherto less well-known work in interpolation from the Russian schools of Yaroslavl and Kazan. One highlight is an extensive list of unsolved problems in interpolation theory, including contributions from a number of experts who were unable to attend the workshop.

A publication of the Bar-Ilan University. Distributed worldwide by the AMS.


Experts in interpolation theory and in various branches of analysis where interpolation is applied.

Table of Contents

  • A. Bernal -- Some results on complex interpolation of \(T_q^p\) spaces
  • Y. A. Brudnyi -- Some recent general results in interpolation theory
  • M. J. Carro and J. Cerdà -- On the interpolation of analytic families of operators
  • F. Cobos and I. Resina -- An interpolation formula for approximation spaces
  • W. C. Connett and A. L. Schwartz -- Interpolation of Banach algebras
  • M. Cwikel and A. Sharif -- Complex interpolation spaces generated by the Gagliardo completion of an arbitrary Banach couple
  • E. Hernández and J. Soria -- Interpolation theorems of some weighted quasi-Banach spaces
  • B. Jawerth and M. Milman -- New results and applications of extrapolation theory
  • B. Jawerth and M. Milman -- Wavelets and best approximation in Besov spaces
  • N. J. Kalton -- On a question of Pisier
  • N. J. Kalton -- Remarks on lattice structure in \(\ell _p\) and \(L_p\) when \(0< p< 1\)
  • R. A. Kerman -- Convergence of approximate identities in weighted Lebesgue spaces
  • M. Mastyło -- Interpolation functors commuting with direct products
  • M. Milman -- Local operators vs Lorentz-Marcinkiewicz spaces
  • I. Ya. Novikov -- Inner estimates
  • B. P. Osilenker -- The generalized \(\Lambda\)-translation in a multiple orthogonal polynomial system
  • V. I. Ovchinnikov -- On the description of interpolation orbits in couples of \(L_p\) spaces when they are not described by the \(K\)-method
  • Y. Raynaud -- On Lorentz-Sharpley spaces
  • R. Rochberg -- A correspondence principle for Toeplitz and Calderon-Toeplitz operators
  • P. A. Shvartsman -- \(K\)-functionals of weighted Lipschitz spaces and Lipschitz selections of multivalued mappings
  • L. V. Veselova and N. M. Zobin -- On a tensor approach to interpolation theory
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