Siberian Mathematical Journal

, Volume 45, Issue 4, pp 722–729 | Cite as

On Embeddings for Classes of Functions with Generalized Smoothness on Metric Spaces

  • A. S. Romanov


Given a metric space with a Borel measure, we consider the classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function summable with some power. We prove embedding theorems for these spaces defined by two different measures satisfying the doubling condition.

metric space measure Sobolev class embedding theorem 


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  1. 1.
    Romanov A. S., “Embedding theorems for a certain function class of Sobolev type on metric spaces,” Sibirsk. Mat. Zh., 45, No. 2, 452–465 (2004).Google Scholar
  2. 2.
    Hajlasz P., “Sobolev spaces on an arbitrary metric space,” Potential Anal., 5, No. 4, 403–415 (1996).Google Scholar
  3. 3.
    Hajlasz P. and Koskela P., “Sobolev met Poincare,” Mem. Amer. Math. Soc., 688, 1–101 (2000).Google Scholar
  4. 4.
    Strömberg J.-O. and Torchinsky A., Weighted Hardy Spaces, Springer-Verlag, Berlin etc. (1989). (Lecture Notes in Mathematics; 1381.)Google Scholar
  5. 5.
    Stein E. M., Singular Integrals and Differentiability Properties of Functions [Russian translation], Mir, Moscow (1973). 729Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • A. S. Romanov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

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