On the Representation of Functions by Absolutely Convergent Series by H -system

DOI10.18500/1816-9791-2018-18-1-49-61zbMath1407.41010OpenAlexW2790439638MaRDI QIDQ3120404

K. A. Navasardyan

Publication date: 4 March 2019

Published in: Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/isu744

zbMATH Keywords

uniform convergenceabsolute convergenceHaar type systemdyadic family

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Convergence and divergence of series and sequences of functions (40A30) Approximation by other special function classes (41A30)

Cites Work

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• Equivalence of Haar bases associated with different dyadic systems
• On the representation of measurable functions by martingales
• A decomposition into atoms of distributions on spaces of homogeneous type
• The representations of functions by orthogonal series possessing martingale properties
• Multiresolution approximations and unconditional bases on weighted Lebesgue spaces on spaces of homogeneous type
• Dyadic Fefferman–Stein inequalities and the equivalence of Haar bases on weighted Lebesgue spaces
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral

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