Strong convergence in the weighted setting of operator-valued Fourier series defined by the Marcinkiewicz multipliers

DOI10.1016/J.CRMA.2015.11.001zbMath1364.42006OpenAlexW2239176222MaRDI QIDQ512346

Earl Berkson

Publication date: 24 February 2017

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2015.11.001

zbMATH Keywords

Fourier seriesshift operatorFourier multiplierAp weight sequenceMarcinkiewicz classmodulus mean-bounded operator

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) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Multipliers in one variable harmonic analysis (42A45)

Cites Work

• Rotation methods in operator ergodic theory
• Extrapolation of weights revisited: new proofs and sharp bounds
• Spectral theory and operator ergodic theory on super-reflexive Banach spaces
• Marcinkiewicz multipliers of higher variation and summability of operator-valued Fourier series

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