Widths of Besov classes of generalized smoothness on the sphere

Authors:
Heping Wang;Sai Tang
Affiliations:
-;-
Venue:
Journal of Complexity
Year:
2012

Citing 5
Cited 0

Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature

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Kolmogorov width of classes of smooth functions on the sphere Sd-1

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Widths of embeddings in function spaces

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Approximation and entropy numbers in Besov spaces of generalized smoothness

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Abstract

We introduce the Besov spaces B"p"@q^@W(S^d^-^1) of generalized smoothness on the sphere S^d^-^1, and obtain the representation theorem, an embedding theorem, and the characterization using a frame. We also study the Kolmogorov, linear and Gelfand widths of Besov classes BB"p"@q^@W(S^d^-^1) of generalized smoothness in L"q(S^d^-^1) for 1@?p,q@?~, and obtain their asymptotic orders.