Abstract
For p∈(−∞, ∞) letQ p (∂Δ) be the space of all complex-valued functions f on the unit circle ∂Δ satisfying
, where the supremum is taken over all subarcs I ⊃ ∂Δ with the arclength |I|. In this paper, we consider some essential properties ofQ p (∂Δ). We first show that if p>1, thenQ p (∂Δ)=BMO(∂Δ), the space of complex-valued functions with bounded mean oscillation on ∂Δ. Second, we prove that a function belongs toQ p (∂Δ) if and only if it is Möbius bounded in the Sobolev spaceL 2 p (∂Δ). Finally, a characterization ofQ p (∂Δ) is given via wavelets.
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Xiao, J., Xiao, J. Some essential properties ofQ p (∂Δ)-spaces. The Journal of Fourier Analysis and Applications 6, 311–323 (2000). https://doi.org/10.1007/BF02511158
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DOI: https://doi.org/10.1007/BF02511158