Unconditional Bases, the Matrix Muckenhoupt Condition, and Carleson Series in a Spectrum
Copyright policy )Unconditional Bases, the Matrix Muckenhoupt Condition, and Carleson Series in a Spectrum
Two families of functions are assigned to a finite system of scalar Muckenhoupt weights on \(\mathbb{R}\). The problem under consideration is if they form unconditional bases in the corresponding spaces. A criterion is obtained for the first family and a sufficient condition for the second one, the both in terms of the corresponding property for rational vector-valued functions. This is done by studying the spectral structure of perturbations of the integration operators and applying two-sided estimates for the Hilbert transform of vector-valued functions. The problem for the rational functions is handled by means of technique of Carleson series.
rational vector-valued functions, Hilbert transform of vector-valued functions, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Completeness of sets of functions in one variable harmonic analysis, spectral structure, Carleson series, integration operators, finite system of scalar Muckenhoupt weights, perturbations, unconditional bases, Banach spaces of continuous, differentiable or analytic functions, Linear operators on function spaces (general), two-sided estimates, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
rational vector-valued functions, Hilbert transform of vector-valued functions, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Completeness of sets of functions in one variable harmonic analysis, spectral structure, Carleson series, integration operators, finite system of scalar Muckenhoupt weights, perturbations, unconditional bases, Banach spaces of continuous, differentiable or analytic functions, Linear operators on function spaces (general), two-sided estimates, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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