Characterization of periodic function spaces via means of Abel-Poisson and Bessel-potential type

DOI10.1016/0021-9045(90)90006-CzbMath0704.42006OpenAlexW2066467504MaRDI QIDQ916944

Hans-Juergen Schmeisser, Winfried Sickel

Publication date: 1990

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(90)90006-c

zbMATH Keywords

rate of convergenceBesov spacesRiesz meansHardy-Littlewood maximal functionAbel-Poisson meansapproximation inequalitiesBessel-potentialinequalities of Nikol'skij typeperiodic Lizorkin-Triebel spacesspaces of Hardy-Sobolev type

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Classical almost periodic functions, mean periodic functions (42A75)

Related Items (6)

Periodic Besov spaces and generalized moduli of smoothness ⋮ Characterization of Besov-Triebel-Lizorkin spaces via approximation by Whittaker's cardinal series and related unconditional Schauder bases ⋮ Moduli of smoothness related to fractional Riesz-derivatives ⋮ Generalized smoothness and approximation of periodic functions in the spaces \(L_p\), \(1 < p < +\infty \) ⋮ Besov spaces with generalized smoothness and summability of multiple Fourier series ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations

Cites Work

• Characterizations of Besov-Hardy-Sobolev spaces: A unified approach
• Equivalence of generalized moduli of continuity
• On strong summability of multiple Fourier series and smoothness properties of functions
• Multipliers for (C,a)-bounded Fourier expansions in Banach spaces and approximation theory
• Strong and best approximation of Fourier series and the Lipschitz classes
• Besov spaces in theory of approximation
• Topics in approximation theory
• Comparison theorems for a generalized modulus of continuity
• Necessary Conditions for the Comparison of Sequences of Linear Functionals
• On Strong Summability of Multiple Fourier Series and Approximation of Periodic Functions
• Periodic Spaces and Relations to Strong Summability of Multiple FOURIER Series
• Some Tauberian theorems with applications to approximation theory
• Some Maximal Inequalities
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