NDLI: Almost Everywhere Convergent Fourier Series

Content Provider	Springer Nature Link
Author	Carro, M. J. Mastyło, M. Rodríguez Piazza, L.
Copyright Year	2011
Abstract	We study some properties of the logconvex quasi-Banach space QA defined by Arias-de-Reyna and show several applications to convergence of Fourier series. In particular, we describe the Banach envelope of QA and prove that there exists a Lorentz space strictly bigger than the Antonov space in which the almost everywhere convergence of the Fourier series holds. We also give a necessary condition for a Banach rearrangement invariant space X to be contained in QA. As an application, we show that for some classes of Banach spaces there is no the largest Banach space in a given class which is contained in QA.
Ending Page	286
Page Count	21
Starting Page	266
File Format	PDF
ISSN	10695869
e-ISSN	15315851
Journal	Journal of Fourier Analysis and Applications
Issue Number	2
Volume Number	18
Language	English
Publisher	SP Birkhäuser Verlag Boston
Publisher Date	2011-10-13
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Almost everywhere convergence Signal, Image and Speech Processing Norms (inequalities, more than one norm, etc.) Fourier series Abstract Harmonic Analysis Rearrangement invariant spaces Mathematical Methods in Physics Fourier Analysis Operator inequalities Lorentz spaces Banach envelope Approximations and Expansions Partial Differential Equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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Almost Everywhere Convergent Fourier Series