Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Higher-dimensional Ahlfors-Beurling type inequalities in Clifford analysis


Author: Mircea Martin
Journal: Proc. Amer. Math. Soc. 126 (1998), 2863-2871
MSC (1991): Primary 31B10, 41A20, 41A63
DOI: https://doi.org/10.1090/S0002-9939-98-04351-2
MathSciNet review: 1451820
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A generalization to higher dimensions of a classical inequality due to Ahlfors and Buerling is proved. As a consequence, an extension of Alexander's quantitative version of Hartogs-Rosenthal Theorem is derived. Both results are stated and proved within the framework of Clifford analysis.


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

  • [AB] L. Ahlfors, and A. Buerling, Conformal invariants and function theoretic null sets, Acta Math. 83 (1950), 101-129. MR 12:171e
  • [A1] H. Alexander, Projections of polynomial hulls, J. Funct. Anal. 13 (1973), 13-19. MR 49:3209
  • [A2] H. Alexander, On the area of the spectrum of an element of a uniform algebra, Complex Approximation Proceedings, Quebec, July 3-8, 1978, Birkhäuser, 1980, pp. 3-12. MR 82b:32015
  • [AS] S. Axler, and J. H. Shapiro, Putnam's theorem, Alexander's spectral area estimate, and VMO, Math. Ann. 271 (1985), 161-183. MR 87b:30053
  • [B] A. Browder, Introduction to Function Algebras, Benjamin, New York, 1969. MR 39:7431
  • [BDS] F. Brackx, R. Delanghe, and F. Sommen, Clifford Analysis, Pitman Research Notes in Mathematics Series, 76, 1982. MR 85j:30103
  • [DSS] R. Delanghe, F. Sommen, and V. Sou\v{c}ek, Clifford Algebra and Spinor-Valued Functions, Kluwer Academic Publishers, 1992. MR 94d:30084
  • [G] T. W. Gamelin, Uniform Algebras, Prentice Hall, 1969. MR 53:14137
  • [GM] J. E. Gilbert and M. A. M. Murray, Clifford Algebras and Dirac Operators in Harmonic Analysis, Cambridge Studies in Advanced Mathematics, 26, Cambridge University Press, 1991. MR 93e:42027
  • [GK] B. Gustafsson and D. Khavinson, On approximation by harmonic vector fields, Houston J. Math. 20 (1994), 75-92. MR 96h:31009
  • [K] D. Khavinson, On uniform approximation by harmonic functions, Mich. Math. J. 34 (1987), 465-473. MR 89a:41026
  • [MSz] M. Martin, and P. Szeptycki, Sharp inequalities for convolution operators with homogeneous kernels and applications, Indiana Univ. Math. J. 46 (1997).
  • [P] M. Putinar, Extreme hyponormal operators, Operator Theory: Advances and Applications, 28, 1988, pp. 249-265. MR 90a:47065
  • [Pu] C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323-330. MR 42:5085
  • [VPY] A. L. Volberg, V. V. Peller, and D. V. Yakubovich, A brief excursion into the theory of hyponormal operators, Algebra i Analiz 2 (1990), 1-30. MR 91i:47034

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 31B10, 41A20, 41A63

Retrieve articles in all journals with MSC (1991): 31B10, 41A20, 41A63


Additional Information

Mircea Martin
Email: mmartin@harvey.bakeru.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04351-2
Keywords: Clifford analysis, approximation theory
Received by editor(s): February 18, 1997
Additional Notes: This work was supported in part by NSF Grant DMS-9301187.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society