Wavelet Approximation and Fourier Widths of Classes of Periodic Functions of Several Variables. I

作者：Bazarkhanov D B^*

来源：Proceedings of the Steklov Institute of Mathematics, 2010, 269(1): 2-24.

DOI：10.1134/S0081543810020021

We obtain characterizations (and prove the corresponding equivalence of norms) of function spaces B(pq)(sm) (I(k)) and L(pq)(sm) (I(k)) of Nikol'skii-Besov and Lizorkin-Triebel types, respectively, in terms of representations of functions in these spaces by Fourier series with respect to a multiple system W(m)(I) of Meyer wavelets and in terms of sequences of the Fourier coefficients with respect to this system. We establish order-sharp estimates for the approximation of functions in B(pq)(sm) (I(k)) and L(pq)(sm) (I(k)) by special partial sums of these series in the metric of L(r)(I(k)) for a number of relations between the parameters s, p, q, r, and m (s = (s(1), ... , s(n)) epsilon R(+)(n), 1 <= p, q, r <= infinity, m - (m(1), ... , m(n)) epsilon N(n), k - m(1) + ... + m(n), and I - R or T). In the periodic case, we study the Fourier widths of these function classes.

• 出版日期2010-7