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Book Review

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Book Information:

Authors: Vladimir G. Maz'ya and Tatyana O. Shaposhnikova
Title: Theory of Sobolev multipliers: with applications to differential and integral operators
Additional book information: Grundlehren der mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), 337, Springer-Verlag, Berlin, 2009, xiv+614 pp., ISBN 978-3-540-69490-8, $139.00, hardcover

References [Enhancements On Off] (What's this?)

  • [Ad] D. R. Adams, On the existence of capacitary strong type estimates in $ R\sp{n}$, Ark. Mat. 14 (1976), 125-140. MR 0417774 (54:5822)
  • [AH] D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, Berlin, 1996. MR 1411441 (97j:46024)
  • [CWW] S. Y. A. Chang, J. M. Wilson, and T.H. Wolff, Some weighted norm inequalities concerning the Schrödinger operators, Comment. Math. Helv. 60 (1985), 217-246. MR 800004 (87d:42027)
  • [Dah] B. E. J. Dahlberg, Regularity properties of Riesz potentials, Indiana Univ. Math. J., 28 (1979), 257-268. MR 523103 (80g:31004)
  • [DH] A. Devinatz and I. I. Hirshman, Multiplier transformations on $ l^{2, \alpha}$, Ann. Math. 69 (1959), 575-587. MR 0104974 (21:3722)
  • [F] C. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206. MR 707957 (85f:35001)
  • [Han] K. Hansson, Imbedding theorems of Sobolev type in potential theory, Math. Scand. 45 (1979), 77-102. MR 567435 (81j:31007)
  • [Hir] I. I. Hirshman, On multiplier transformations, II, Duke Math. J. 28 (1961), 45-56. MR 0124693 (23:A2004)
  • [KS] R. Kerman and E. Sawyer, The trace inequality and eigenvalue estimates for Schrödinger operators, Ann. Inst. Fourier, Grenoble 36 (1987), 207-228. MR 867921 (88b:35150)
  • [M1] V. G. Maz'ya, Classes of domains and embedding theorems for functional spaces, Dokl. Akad. Nauk SSSR, 133 (1960), 527-530. MR 0126152 (23:A3448)
  • [M2] V. G. Maz'ya, On the theory of the $ n$-dimensional Schrödinger operator, Izv. Akad. Nauk SSSR, Ser. Matem., 28 (1964), 1145-1172. MR 0174879 (30:5070)
  • [M3] V. G. Maz'ya, Sobolev Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1985 (new edition in press). MR 817985 (87g:46056)
  • [MV] V. G. Maz'ya and I. E. Verbitsky, Form boundedness of the general second order differential operator, Comm. Pure Appl. Math. 59 (2006), 1286-1329. MR 2237288 (2008d:47089)
  • [P] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Press, Durham, NC, 1976. MR 0461123 (57:1108)
  • [Pol] J. C. Polking, A Leibniz formula for some differential operators of fractional order, Indiana Univ. Math. J. 27 (1972), 1019-1029. MR 0318868 (47:7414)
  • [RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics. II: Fourier Analysis, Self-Adjointness, Academic Press, New York-London, 1975. MR 0493420 (58:12429b)
  • [RSS] G. V. Rozenblum, M. A. Shubin, and M. Z. Solomyak, Spectral Theory of Differential Operators, Encyclopaedia of Math. Sci., 64. Partial Differential Equations VII. (M. A. Shubin, editor). Springer-Verlag, Berlin-Heidelberg, 1994. MR 1313735 (95j:35156)
  • [Str] R. S. Strichartz, Multipliers of fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060. MR 0215084 (35:5927)
  • [V] I. E. Verbitsky, Nonlinear potentials and trace inequalities, The Maz'ya Anniversary Collection, Vol. 2. Operator Theory Adv. Appl. 110, Birkhäuser, Basel (1999), 323-343. MR 1747901 (2001g:46086)

Review Information:

Reviewer: I. E. Verbitsky
Affiliation: Columbia, Missouri
Journal: Bull. Amer. Math. Soc. 48 (2011), 101-105
MSC (2000): Primary 26D10, 46E25, 42B25; Secondary 35J10, 35J25
Published electronically: March 10, 2010
Additional Notes: The author was partially supported by NSF Grant DMS-0901550.
Review copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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