We point out that the well known characterization of LP spaces (1 < p < infinity) in terms of orthogonal wavelet bases extends to any separable rearrangement invariant Banach function space X on R-n (equipped with Lebesgue measure) with nontrivial Boyd's indices: Moreover we show that such bases are unconditional bases of X
Soardi, P. (1997). Wavelet bases in rearrangement invariant function spaces. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 125(12), 3669-3673 [10.1090/S0002-9939-97-04207-X].
Wavelet bases in rearrangement invariant function spaces
Soardi, PM
1997
Abstract
We point out that the well known characterization of LP spaces (1 < p < infinity) in terms of orthogonal wavelet bases extends to any separable rearrangement invariant Banach function space X on R-n (equipped with Lebesgue measure) with nontrivial Boyd's indices: Moreover we show that such bases are unconditional bases of X
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