On unconditional basis property in the space \(H^1(\mathbb R)\) of a system of Franklin functions with vanishing means

DOI10.3103/S1068362316060030zbMath1405.42050MaRDI QIDQ528874

K. A. Keryan

Publication date: 17 May 2017

Published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences (Search for Journal in Brave)

zbMATH Keywords

Franklin systemunconditional basis\(H^1\) space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Uniqueness and localization for orthogonal series (42C25)

Related Items (1)

Orthonormal spline systems on \(\mathbb R\) with zero means as bases in \(H^1(\mathbb R)\)

Cites Work

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• General periodic Franklin system as a basis in \(H^1[0,1\)]
• The Franklin system is an unconditional basis in \(H_ 1\)
• Some inequalities for Franklin series
• Projections onto piecewise linear functions
• On a system of piecewise linear functions with vanishing integrals on \(R\)
• Extensions of Hardy spaces and their use in analysis
• General Franklin systems as bases in H¹[0,1]
• Unconditionality of general Franklin systems in L^p[0,1, 1<p<∞]
• Unconditionality of orthogonal spline systems in H¹
• Anisotropic Franklin bases on polygonal domains
• Properties of the orthonormal Franklin system, II
• Properties of the orthonormal Franklin system
• The \(L_\infty\)-norm of the \(L_2\)-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture

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