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In this paper we extend the result established for the euclidean space in [3] to the hyperbolic disk. This includes the reconstruction of a function defined in a fixed disk B(0,R) from its averages on disks of radii r1, r2 lying in B(0, R).
We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderón-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.
Let be a symmetric space of the noncompact type, with Laplace–Beltrami operator , and let be the -spectrum of . For in
such that , let be the operator on
defined formally as . In this paper, we
obtain operator norm estimates for for all , and show
that these are optimal when is small and when is
bounded below .
The author establishes the localization principle for the Triebel-Lizorkin spaces on spaces of homogeneous type.
Currently displaying 141 –
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