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Theory and Applications of Differentiable Functions of Several Variables. 16
Edited by: S. M. Nikolskiĭ

Proceedings of the Steklov Institute of Mathematics
1994; 260 pp; softcover
Volume: 204
ISBN-10: 0-8218-0276-3
ISBN-13: 978-0-8218-0276-2
List Price: US$229
Member Price: US$183.20
Order Code: STEKLO/204
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This book explores various topical trends in the theory of differentiable functions of several real variables and its applications. Among the subjects covered are: imbedding of various spaces of differentiable functions defined on sets in Euclidean space, on a sphere, and in a polydisc; approximation of functions; estimates for the norms of various integral operators in weighted space; conditions for stabilization of a function to a polynomial; sufficient conditions for multipliers; construction of unconditional bases in anisotropic spaces; existence of entire solutions for quasilinear equations; and establishment of an asymptotic formula for the kernels of powers of the resolvent of elliptic operators.


Research mathematicians.

Table of Contents

  • E. I. Berezhnoĭ -- Sharp estimates for operators on cones in ideal spaces
  • M. Z. Berkolaĭko and I. Ya. Novikov -- Unconditional bases in spaces of functions of anisotropic smoothness
  • K. Kh. Boĭmatov -- Asymptotic behavior of the Green function of parabolic equations and of the kernels of complex powers of the resolvent of elliptic operators
  • V. I. Burenkov and V. A. Gusakov -- On precise constants in Sobolev imbedding theorems. III
  • V. I. Burenkov and M. Sh. Tuyakbaev -- On Fourier integral multipliers in weighted \(L_{p}\)-spaces with an exponential weight. II
  • V. S. Guliev -- Two-weighted inequalities for integral operators in \(L_p\)-spaces, and their applications
  • V. S. Guliev and P. I. Lizorkin -- Classes of holomorphic and harmonic functions in the polydisk in connection with their boundary values
  • G. A. Kalyabin -- Pointwise multipliers in certain Sobolev spaces containing unbounded functions
  • L. D. Kudryavtsev -- On some inequalities for functions and their derivatives on an infinite interval
  • P. I. Lizorkin and Kh. P. Rustamov -- Nikol'skiĭ-Besov spaces on the sphere in connection with approximation theory
  • S. M. Nikol'ski -- More on approximation by entire functions of exponential type and by polynomials
  • Yu. S. Nikol'ski -- Imbedding theorems for anisotropic weighted spaces of differentiable functions on open sets
  • R. Oĭarov -- Two-sided norm estimates for certain classes of integral operators
  • S. I. Pokhozhaev -- On entire radial solutions of quasilinear elliptic equations
  • Kh. P. Rustamov -- On equivalence of different moduli of smoothness on the sphere
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