Abstract
This chapter contains a local analysis of Q p(T) based on the dyadic portions. First of all, we give an alternate characterization of Q p in terms of the square mean oscillations over successive bipartitions of arcs in T. Next, we consider the dyadic counterpart Q p d(T) of Q p(T), in particular, we show that f ∈ Q p(T) if and only if (almost) all its translates belong to Q d p(T); conversely, functions in Q p(T) may be obtained by averaging translates of functions in Q p(T). Finally, as a natural application of the dyadic model of Q p(T), we present a wavelet expansion theorem of Q p(T).
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). Dyadic Localization. In: Xiao, J. (eds) Holomorphic Q Classes. Lecture Notes in Mathematics, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45434-9_8
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DOI: https://doi.org/10.1007/3-540-45434-9_8
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42625-7
Online ISBN: 978-3-540-45434-2
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