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   -> Volume 7, Issue 5

Question: Jackson-type inequality (simultaneous approximation)
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Eric von Lieres (

PostPosted: Wed Apr 22, 1998 8:42 pm    
Subject: Question: Jackson-type inequality (simultaneous approximation)
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#35 Question: Jackson-type inequality (simultaneous approximation)

Dear Waveletters and Approximators,

For my diploma thesis I need a Jackson-type inequality of the form

||f - P_j f||_W_m_p <= C 2^-((s-m) j) ||f||_W_s_p

where ||.||_W_m_p is the usual Sobolev-Norm on R^d with 1 < p <
infinity and m,s,d integer. P_j denotes the (orthogonal) projector on
the principal shift-invariant approximation space V_j concerning to
the multiresolution-analysis generated by a single scaling-function

I use the compactly supported wavelets of I. Daubechies with some
regularity and those of Y. Meyer wich decay faster than every inverse

I know a proof for the case p=2, but it involves fourier-techniques, which
are not that easy to handle in the general case.

Does anyone know results of the requested kind? Hints leading in this
direction are appreciated, too.

Thanks in advance.

Eric von Lieres
Fachbereich Mathematik
Uni-GH Siegen
Hoelderlinstrasse 6
57068 Siegen
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