East Asian mathematical journal

  • 제28권1호
  • /
  • Pages.73-79
  • /
  • 2012
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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CHARACTERIZATION OF LIPSCHITZ-TYPE FUNCTIONS BY GARSIA-TYPE NORMS ON THE UPPER HALF SPACE

  • Byun, Ji-Soo (Department of Mathematics Education, Kyungnam University) ;
  • Cho, Hong-Rae (Department of Mathematics, Pusan National University) ;
  • Im, Bong-Hak (Department of Mathematics, Pusan National University)
  • 투고 : 2011.10.06
  • 심사 : 2012.01.11
  • 발행 : 2012.01.31
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초록

It is well-known that the BMO norm is equivalent to the Garsia norm. In this paper, we characterize mean-Lipschitz spaces by using Garsia-type norms on the upper half space $\mathbb{R}_+^{n+1}$.

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참고문헌

  1. Sh. Axler and J. Shapiro, Putman's theorem, Alexander's spectral area estimate and VMO, Math. Ann. 271(1985), 161-183. https://doi.org/10.1007/BF01455985
  2. J. B. Garnett, Bounded Analytic Functions, Academic Press, Orlando, Fla., 1981.
  3. A. Garsia, A presentation of Fefferman's theorem, Unpublished notes, 1971.
  4. E. M. Stein, Singular Integral and Differentiablity Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.