Affine Synthesis onto Lebesgue and Hardy Spaces
نویسنده
چکیده
The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R) under mild conditions on the synthesizer ψ ∈ L(R), 1 ≤ p < ∞, with R Rd ψ dx = 1. Here ψj,k(x) = |det aj |ψ(ajx−k), and the dilation matrices aj expand, for example aj = 2I . Affine synthesis further maps a discrete mixed Hardy space `(h) onto H(R). Therefore the H-norm of a function is equivalent to the infimum of the norms of the sequences representing the function in the affine system: ‖f‖H1 ≈ inf { X
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Affine Synthesis and Coefficient Norms for Lebesgue, Hardy and Sobolev Spaces
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