Proceedings of the Steklov Institute of Mathematics 1994; 265 pp; softcover Volume: 194 ISBN10: 0821831526 ISBN13: 9780821831526 List Price: US$224 Member Price: US$179.20 Order Code: STEKLO/194
 This colletion is the fourteenth in an ongoing series on differentiable functions of several variables, presenting recent contributions to a line of research begun by Sobolev in 1950. The papers study various spaces of differentiable functions of several real variables in Euclidean space, their imbeddings, equivalent normings, weighted estimates of derivatives, and traces on sets. Several questions of approximation in function spaces on the line, on a hyperboloid, and on Lobachevsky space are studied. Investigations of bilinear approximations are applied to estimates of the singular numbers of integral operators and widths. The authors also examine the asymptotics of the spectrum of elliptic systems, as well as the Dirichlet variational problem for a degenerate elliptic operator. Finally, a block method of solving Laplace's equation for nonanalytic boundary conditions is developed. Readership Workers in function spaces and partial differential equations. Table of Contents  P. M. Badzhrachariya and V. I. Burenkov  Necessary and sufficient conditions for continuity with respect to a nonlinear translation for various function spaces
 O. V. Besov  Equivalent normings of the SobolevLiouville space on a domain
 K. Kh. Boĭmatov  A Tauberian method for studying spectral asymptotics of strongly degenerate elliptic systems
 V. I. Burenkov  On the best constant in Hardy's inequality with \(0< p< 1\) for monotone functions
 E. A. Volkov  Approximate solution of Laplace's equation by the block method on polygons under nonanalytic boundary conditions
 M. A. Gabidzashvili, I. Z. Genebashvili, and V. M. Kokilashvili  Twoweight inequalities for generalized potentials
 P. A. Zharov  On a twoweight inequality. Generalization of inequalities of Hardy and Poincaré
 V. A. Ivanov  Precise results in the problem of the BernsteinNikol'skiĭ inequality on compact symmetric Riemannian spaces of rank 1
 P. I. Lizorkin  Direct and inverse theorems of approximation theory for functions on Lobachevsky space
 G. G. MagarilIl'yaev  On best approximation by splines of function classes on the line
 G. A. Mamedov  On traces of functions from anisotropic Nikol'skiĭBesov and LizorkinTriebel spaces on subsets of Euclidean space
 N. V. Miroshin  The exterior Dirichlet variational problem for an elliptic operator with degeneration
 Yu. S. Nikol'skiĭ  Imbedding theorems for nonisotropic weighted spaces of differentiable functions on unbounded domains
 I. V. Petrova  Approximation on a hyperboloid in the \(L_2\)metric
 V. N. Temlyakov  Bilinear approximation and related questions
