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The smoothness of functions f in the space Lp(R) with 1&lt;p&lt;∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform.

Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in Lp(R)