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CHARACTERIZATION OF LIPSCHITZ-TYPE FUNCTIONS BY GARSIA-TYPE NORMS ON THE UPPER HALF SPACE

  • Received : 2011.10.06
  • Accepted : 2012.01.11
  • Published : 2012.01.31

Abstract

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 $\mathbb{R}_+^{n+1}$.

Keywords

upper half space;BMO;mean-Lipschitz spaces;Garsia-type norm

References

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  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 A. Garsia, A presentation of Fefferman's theorem, Unpublished notes, 1971.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.