Hilbert Transform of a Wavelet System: Boundedness of Orthogonal Projections in the Uniform Norm

摘要

Let ψ be a wavelet associated with a scaling function ψ, and let φ be the Hilbert transform of ψ. Under some natural conditions on the smoothness and decay of φ, we show that the orthogonal projections onto the spaces generated by ψ are bounded in the uniform norm.