论文信息 - Asymptotic regularity of Daubechies’ scaling functions

Asymptotic regularity of Daubechies’ scaling functions

Let N , N 1, be Daubechies' scaling function with symbol 1+e i 2 N QN (), and let sp(N ); 0 <p 1, be the corresponding L p Sobolev exponent. In this paper, we make a sharp estimation of sp(N ), and we prove that there exists a constant C independent of N such that N lnjQN (2=3)j ln 2 C N sp(N ) N lnjQN(2=3)j ln 2 : This answers a question of Cohen and Daubeschies (Rev. Mat. Iberoameri- cana, 12(1996), 527-591) positively.

Qiyu Sun | Ka-Sing Lau

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