Abstract
The paper deals with unconditional wavelet bases in weighted spaces. Inhomogeneous wavelets of Daubechies type are considered. Necessary and sufficient conditions for weights are found for which the wavelet system is an unconditional basis in weighted spaces in dependence on .
Highlights
Wavelet systems in weighted Lp spaces were investigated by several authors
The main Theorem of the paper asserts that the inhomogeneous wavelet system of Daubechies type is an unconditional basis in Lp dμ if and only if dμ wdx with w ∈ Aploc
Let us recall the definition of Muckenhoupt weights, compare 10
Summary
He proved that the homogeneous wavelet system of Daubechies type is an unconditional basis in Lp Rn, dμ , 1 < p < ∞, if and only if dμ wdx, where w is a weight belonging to the Muckenhoupt class Ap. He proved that the homogeneous wavelet system of Daubechies type is an unconditional basis in Lp Rn, dμ , 1 < p < ∞, if and only if dμ wdx, where w is a weight belonging to the Muckenhoupt class Ap He found a sufficient and necessary condition for inhomogeneous systems to be unconditional bases. The main Theorem of the paper asserts that the inhomogeneous wavelet system of Daubechies type is an unconditional basis in Lp dμ if and only if dμ wdx with w ∈ Aploc
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