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Theory and Applications of Differentiable Functions of Several Variables. 14
Edited by: S. M. Nikol'skiĭ
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Proceedings of the Steklov Institute of Mathematics
1994; 265 pp; softcover
Volume: 194
ISBN-10: 0-8218-3152-6
ISBN-13: 978-0-8218-3152-6
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.

Workers in function spaces and partial differential equations.

• 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 Sobolev-Liouville 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 -- Two-weight inequalities for generalized potentials
• P. A. Zharov -- On a two-weight inequality. Generalization of inequalities of Hardy and Poincaré
• V. A. Ivanov -- Precise results in the problem of the Bernstein-Nikol'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. Magaril-Il'yaev -- On best approximation by splines of function classes on the line
• G. A. Mamedov -- On traces of functions from anisotropic Nikol'skiĭ-Besov and Lizorkin-Triebel 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